Area
Formulas on Area
1
1) Area of Triangle = --------- X base X height
2
2) Area of Triangle = √s(s-a)(s-b)(s-c)
where a, b, c are sides of Triangle
a+b+c
and semi perimeter S = -----------------------
2
√3
3) Area of an equilateral Triangle = ------------ X (Side)2
4 (x + y + z )2
4) Area of an Equilateral Triangle = -------------------
√3
Where x, y, z are Perpendiculars .
1
5) Area of Isosceles Triangle = ----- X ( Equal Side)2
2
6) Area of Rectangle = Length X Breadth
7) Area of four wall = 2( Length X Breadth ) Height
8) Area of Square = ( Side )2
9) Area of Parallelogram = Base X Height
1
10) Area of Trapezium = ------------ ( a + b ) h
2
where a & b are parallel side , h distance between parallel line.
1
11) Area of Rhombus = --------( d1X d2)
2
Where d1 & d2 are diagonals
12) Area of Circle = πr2
13) Circumference of Circle = 2πr
πR 2 0
14) Area of a Sector = -----------------
360°
2πR 0
15) Length of Arc = -------------
360°
Example :
1) One side of a rectangular field is 12 m and one of its diagonals is 13 m. Find the area of the field .
Solution :
It has right triangle hence by Pythagoras Theorem
Breadth of rectangle =√ (13)2-(12)2 = 5 m
Area = Length X Breadth
= (12 X 5 )
= 60 m2
2) Obtain the area of an isosceles triangle, in which each one of equal sides is 5 m and the third side 6 m.
Solution.
where a =5 , b = 5 , c = 6
a+b+c 5 + 5 + 6
S = -------------- = ---------------------- = 8
2 2
Area = √s(s-a)(s-b)(s-c)
= √8(8-5)(8-5)(8-6)
= √144
= 12 m2
3)The base of a triangular field is three times its altitude. If the cost of harvesting the field at Rs. 240 per hectare be Rs. 3240, find its base and height.
Solution
Total cost 3240
Area of field = --------------------- = ------------------- hectares
Rate 240
= 13.5 X 10000 = 135000 m2
4) The diameter of the wheel of a car is 140 cm. How many revolutions per minute the wheel make in order to keep a speed of 66 km per hour ?
Solution
Covered Distance in 1 minute
66X1000X100
= --------------------------- cm = 110000 cm
60
Distance Covered in 1 revolution
22
Circumference of wheel = 2 X ---------X 70 cm = 440 cm
7
110000
Number of revolutions = ----------------------- = 250
400
5) A rectangular plot is 116 m by 68 m. It has tiles path 2.5 m wide all around it on the inside. Find the area of the path .
Solution
Area of the plot = 116 X 68
= 7888 m2
Area of the plot excluding the path
= [(116 - 5) X (68 -51) ]
= 111 X 63
= 6993 m2
Exercise
1) The length of a rectangle is 2 cm more than its breadth. The perimeter is 48 cm. the area of the rectangle ( in cm2) is :
a) 96 b) 128 c) 143 d) 144
2)If the perimeter of a rectangular field is 200 m and its breadth is 40 m, then its area ( in m2 ) is:
a) 1200 b) 2400 c) 4800 d) 6000
3)Around a rectangular garden of length 10 m and width 5 m, a road 1 m wide is laid. The cost of metalling the road at Rs. 200 per m2 is
a) Rs. 3400 b) Rs. 6000 c) Rs. 6800 d) Rs. 13200
4)Within a rectangular garden 10 m wide and 20 m long, we wish to pave a walk around the borders of uniform width so as to leave an area of 96 sq. meters for flowers. How wide should the walk be ?
a) 1 m b) 2 m c) 2.1 m d) 2.5 m
5) The length of a rectangle is twice its breadth.If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 cm2 . Then the rectangle is :
a) 20 cm b) 30 cm c) 40 cm d) 50 cm
6)The cost of levelling a rectangular ground at Rs. 1.25 per sq. meter is Rs. 900. If the length of the ground is 30 meters, then the width is :
a) 330 meters b) 34 meters c) 24 meters d) 18 meters
7) The area of rectangular field is 52000 m2. This rectangular area has been drawn on a map to the scale 1 cm to 100 m. The length is shown as 3.25 cm on the map. The breadth of the rectangular field is :
a) 300.5 m b) 200.5 m c) 160 m d) 150 m
8) If the side of square is doubled, then the ratio of the resulting square to that of the given square is :
a) 1: 2 b) 2: 1 c) 3: 1 d) 4 : 1
9) The number of marble slabs of size 20 cm X 30 cm required to pave the floor of a square room of side 3 m , is :
a) 150 b) 100 c) 25 d) 225
10) If the length of diagonal AC of a square ABCD is 5.2 cm, The area of square ABCD is
a) 15.12 sq. cm b)13.52 sq.cm c)12.62 sq.cm d) 10 sq.cm
Answer
1) c 2) b 3) c 4) b 5) c 6) c 7) c 8) d 9) a 10) b
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