{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 24: Area of plane figures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.1, Page number 24.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of triangle is 150.0 cm**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "b=15;     #base(cm)\n",
    "h=20;     #altitude(cm)\n",
    "\n",
    "#Calculation\n",
    "A=b*h/2;    #area of triangle(cm**2)\n",
    "\n",
    "#Result\n",
    "print \"area of triangle is\",A,\"cm**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.2, Page number 24.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "perpendicular length is 10.0 cm\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "A=205;    #area of triangle(cm**2)\n",
    "s=41;     #side(cm)\n",
    "\n",
    "#Calculation\n",
    "p=2*A/s;    #perpendicular length(cm)\n",
    "\n",
    "#Result\n",
    "print \"perpendicular length is\",p,\"cm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.3, Page number 24.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area is 6 *math.sqrt(6) cm**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=5;\n",
    "b=6;\n",
    "c=7;       #sides of triangle(cm)\n",
    "\n",
    "#Calculation\n",
    "s=(a+b+c)/2;     #semi perimeter(cm)\n",
    "A=math.sqrt(s*(s-a)*(s-b)*(s-c));    #base area(cm**2)\n",
    "\n",
    "#Result\n",
    "print \"area is\",int(A/math.sqrt(6)),\"*math.sqrt(6) cm**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.4, Page number 24.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area is 6.928 cm**2\n",
      "perimeter is 12 cm\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=4;     #side of triangle(cm)\n",
    "\n",
    "#Calculation\n",
    "A=math.sqrt(3)*a**2/4;    #area(cm**2)\n",
    "P=3*a;      #perimeter(cm)\n",
    "\n",
    "#Result\n",
    "print \"area is\",round(A,3),\"cm**2\"\n",
    "print \"perimeter is\",P,\"cm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.5, Page number 24.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area is 60.0 cm**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "b=10;    #base(cm)\n",
    "a=13;    #side(cm)\n",
    "\n",
    "#Calculation\n",
    "A=b*math.sqrt((4*a**2)-(b**2))/4;    #area(cm**2)\n",
    "\n",
    "#Result\n",
    "print \"area is\",A,\"cm**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.6, Page number 24.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "length of each side is 32.0 cm\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "P=100;    #perimeter(cm)\n",
    "b=36;     #base(cm)\n",
    "\n",
    "#Calculation\n",
    "a=(P-b)/2;       #length of each side(cm)\n",
    "\n",
    "#Result\n",
    "print \"length of each side is\",a,\"cm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.7, Page number 24.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of triangle is 200.0 cm**2\n",
      "perimeter of triangle is 68.3 cm\n",
      "answer given in the book is wrong\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "l=20;      #length of one leg(cm)\n",
    "\n",
    "#Calculation\n",
    "A=l**2/2;     #area of triangle(cm**2)\n",
    "P=l*(2+math.sqrt(2));     #perimeter of triangle(cm)\n",
    "\n",
    "#Result\n",
    "print \"area of triangle is\",A,\"cm**2\"\n",
    "print \"perimeter of triangle is\",round(P,1),\"cm\"\n",
    "print \"answer given in the book is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.8, Page number 24.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "length of hypotenuse is 13.0 cm\n",
      "area of triangle is 30.0 cm**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "l1=12;     #length of one leg(cm)\n",
    "l2=5;      #length of another leg(cm)\n",
    "\n",
    "#Calculation\n",
    "h=math.sqrt(l1**2+l2**2);     #length of hypotenuse(cm)\n",
    "A=l1*l2/2;      #area of triangle(cm**2)\n",
    "\n",
    "#Result\n",
    "print \"length of hypotenuse is\",h,\"cm\"\n",
    "print \"area of triangle is\",A,\"cm**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.9, Page number 24.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of rectangle is 720 cm**2\n",
      "perimeter of rectangle is 112 cm\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "l=36;     #length(cm)\n",
    "b=20;     #breadth(cm)\n",
    "\n",
    "#Calculation\n",
    "A=l*b;     #area of rectangle(cm**2)\n",
    "P=2*(l+b);    #perimeter of rectangle(cm)\n",
    "\n",
    "#Result\n",
    "print \"area of rectangle is\",A,\"cm**2\"\n",
    "print \"perimeter of rectangle is\",P,\"cm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.10, Page number 24.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of rectangle is 60.0 cm**2\n",
      "perimeter of rectangle is 34.0 cm\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "l=12;      #length of rectangle(cm)\n",
    "d=13;      #diagonal of rectangle(cm)\n",
    "\n",
    "#Calculation\n",
    "A=l*math.sqrt(d**2-l**2);     #area of rectangle(cm**2)\n",
    "P=2*(l+math.sqrt(d**2-l**2));    #perimeter of rectangle(cm)\n",
    "\n",
    "#Result\n",
    "print \"area of rectangle is\",A,\"cm**2\"\n",
    "print \"perimeter of rectangle is\",P,\"cm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.11, Page number 24.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "diagonal of rectangle is 25.0 cm\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "l=20;     #length(cm)\n",
    "b=15;     #breadth(cm)\n",
    "\n",
    "#Calculation\n",
    "d=math.sqrt(l**2+b**2);      #diagonal of rectangle(cm)\n",
    "\n",
    "#Result\n",
    "print \"diagonal of rectangle is\",d,\"cm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.12, Page number 24.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of rectangle is 12.0 cm**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "P=14;      #perimeter of rectangle(cm)\n",
    "d=5;       #diagonal(cm)\n",
    "\n",
    "#Calculation\n",
    "A=((P**2/4)-(d**2))/2;     #area of rectangle(cm**2)\n",
    "\n",
    "#Result\n",
    "print \"area of rectangle is\",A,\"cm**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.13, Page number 24.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "length of rectangle is 24.0 cm\n",
      "breadth of rectangle is 10.0 cm\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "P=68;      #perimeter of rectangle(cm)\n",
    "A=240;     #area of rectangle(cm**2)\n",
    "\n",
    "#Calculation\n",
    "l=A/10;     #length of rectangle(cm)\n",
    "y=P/2;\n",
    "b=y-l;      #breadth of rectangle(cm)\n",
    "\n",
    "#Result\n",
    "print \"length of rectangle is\",l,\"cm\"\n",
    "print \"breadth of rectangle is\",b,\"cm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.14, Page number 24.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area is 100 cm**2\n",
      "perimeter is 40 cm\n",
      "diagonal is 14.14 cm\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=10;     #side of square(cm)\n",
    "\n",
    "#Calculation\n",
    "A=a**2;     #area(cm**2)\n",
    "P=4*a;      #perimeter(cm)\n",
    "d=a*math.sqrt(2);     #diagonal(cm)\n",
    "\n",
    "#Result\n",
    "print \"area is\",A,\"cm**2\"\n",
    "print \"perimeter is\",P,\"cm\"\n",
    "print \"diagonal is\",round(d,2),\"cm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.15, Page number 24.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "diagonal is 900 m\n",
      "perimeter is 120.0 m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "A=900;     #area(m**2)\n",
    "\n",
    "#Calculation\n",
    "d=math.sqrt(2*A);     #diagonal(m)\n",
    "P=math.sqrt(16*A);    #perimeter(m) \n",
    "\n",
    "#Result\n",
    "print \"diagonal is\",A,\"m\"\n",
    "print \"perimeter is\",P,\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.16, Page number 24.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area is 200.0 cm**2\n",
      "perimeter is 56.569 cm\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d=20;     #diagonal(cm)\n",
    "\n",
    "#Calculation\n",
    "A=d**2/2;     #area(cm**2)\n",
    "P=math.sqrt(16*A);    #perimeter(cm)\n",
    "\n",
    "#Result\n",
    "print \"area is\",A,\"cm**2\"\n",
    "print \"perimeter is\",round(P,3),\"cm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.17, Page number 24.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area is 600.0 m**2\n",
      "perimeter is 100.0 m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d1=40;      #first diagonal(m)\n",
    "d2=30;      #second diagonal(m)\n",
    "\n",
    "#Calculation\n",
    "A=d1*d2/2;     #area(m**2)\n",
    "P2=4*(d1**2+d2**2);    \n",
    "p=math.sqrt(P2);    #perimeter(m)\n",
    "\n",
    "#Result\n",
    "print \"area is\",A,\"m**2\"\n",
    "print \"perimeter is\",p,\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.18, Page number 24.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of rhombus is 260 cm**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=13;      #side of rhombus(cm)\n",
    "h=20;      #height of rhombus(cm)\n",
    "\n",
    "#Calculation\n",
    "A=a*h;    #area of rhombus(cm**2)\n",
    "\n",
    "#Result\n",
    "print \"area of rhombus is\",A,\"cm**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.19, Page number 24.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of rhombus is 300.0 m**2\n",
      "perimeter of rhombus is 100.0 m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=25;      #side of rhombus(m)\n",
    "h=40;      #height of rhombus(m)\n",
    "\n",
    "#Calculation\n",
    "A=d*math.sqrt((a**2)-((h/2)**2));      ##area of rhombus(m**2)\n",
    "P=4*a;      #perimeter of rhombus(m)\n",
    "\n",
    "#Result\n",
    "print \"area of rhombus is\",A,\"m**2\"\n",
    "print \"perimeter of rhombus is\",p,\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.20, Page number 24.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of quadrilateral is 120.0 m**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d=12;      #diagonal(cm)\n",
    "p1=13;     #length of offset 1(cm)\n",
    "p2=7;      #length of offset 2(cm)\n",
    "\n",
    "#Calculation\n",
    "A=d*(p1+p2)/2;    #area of quadrilateral(m**2)\n",
    "\n",
    "#Result\n",
    "print \"area of quadrilateral is\",A,\"m**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.21, Page number 24.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of parallelogram is 600 m**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d=30;      #length of diagonal(m)\n",
    "l=20;      #length of perpendicular(m)\n",
    "\n",
    "#Calculation\n",
    "A=d*l;    #area of parallelogram(m**2)\n",
    "\n",
    "#Result\n",
    "print \"area of parallelogram is\",A,\"m**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.22, Page number 24.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of parallelogram is 151.789 m**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=12;     #length of side 1(m)\n",
    "b=14;     #length of side 2(m)\n",
    "d=22;     #length of diagonal(m)\n",
    "\n",
    "#Calculation\n",
    "S=(a+b+d)/2;    #semi perimeter(m)\n",
    "A=2*math.sqrt(S*(S-a)*(S-b)*(S-d));     #area of parallelogram(m**2)\n",
    "\n",
    "#Result\n",
    "print \"area of parallelogram is\",round(A,3),\"m**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.23, Page number 24.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "length of second diagonal is 18.0 m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=13;     #length of side 1(m)\n",
    "b=11;     #length of side 2(m)\n",
    "d1=16;     #length of diagonal 1(m)\n",
    "\n",
    "#Calculation\n",
    "d22=(2*(a**2+b**2))-(d1**2);    \n",
    "d2=math.sqrt(d22);      #length of second diagonal(m)\n",
    "\n",
    "#Result\n",
    "print \"length of second diagonal is\",d2,\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.24, Page number 24.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of trapezium is 270.0 m**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=20;     #length of parallel side 1(m)\n",
    "b=25;     #length of parallel side 2(m) \n",
    "h=12;     #distance(m)\n",
    "\n",
    "#Calculation\n",
    "A=(a+b)*h/2;   #area of trapezium(m**2)\n",
    "\n",
    "#Result\n",
    "print \"area of trapezium is\",A,\"m**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.25, Page number 24.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of trapezium is 5673.66 m**2\n",
      "answer varies due to rounding off errors\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=120;     #length of parallel side 1(m)\n",
    "b=75;     #length of parallel side 2(m) \n",
    "c=105;     #length of non parallel side 1(m)\n",
    "d=72;     #length of non parallel side 2(m) \n",
    "\n",
    "#Calculation\n",
    "K=a-b;    #difference of parallel sides(m)\n",
    "S=(K+c+d)/2;    #semi perimeter(m)\n",
    "x=S*(S-K)*(S-c)*(S-d);    \n",
    "A=(a+b)*math.sqrt(x)/K;    #area of trapezium(m**2)\n",
    "\n",
    "#Result\n",
    "print \"area of trapezium is\",round(A,2),\"m**2\"\n",
    "print \"answer varies due to rounding off errors\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.26, Page number 24.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of circle is 616.0 m**2\n",
      "circumference of circle is 88.0 m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "r=14;     #radius(m)\n",
    "\n",
    "#Calculation\n",
    "C=2*math.pi*r;     #circumference of circle(m)\n",
    "A=math.pi*r**2;    #area of circle(m**2)\n",
    "\n",
    "#Result\n",
    "print \"area of circle is\",round(A),\"m**2\"\n",
    "print \"circumference of circle is\",round(C),\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 24.27, Page number 24.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of circle is 154.0 m**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "C=44;     #circumference of circle(m)\n",
    "\n",
    "#Calculation\n",
    "A=C**2/(4*math.pi);    #area of circle(m**2)\n",
    "\n",
    "#Result\n",
    "print \"area of circle is\",round(A),\"m**2\""
   ]
  }
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