In mathematics the area of a plane figure refers to the number of square units the figure covers. The area is the inside shape or space measured in square units. In rectangles and in squares, a simple calculation of length times width will give the number of square units. The square units could be inches, centimeters, yards etc. or whatever the requested unit of measure asks for. There are many formulas used to determine the area of many common shapes or polygons.
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
Perimeter = Distance covered in 8 min. = \(12000\times 8\over60\) m = 1600 m
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m2.
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = \(404\times100\over100\times 100\) % = 4.04%
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
\(2(l+b)\over b\) = 5
2l + 2b = 5b
3b = 2l
b = \(2\over3\) l
Then, Area = 216 cm2
l x b = 216
l x \(2\over3\)l = 216
l2 = 324
l = 18 cm.
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
Area of the park = (60 x 40) m2= 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2= 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.