Page 236 - Start Up Mathematics_7

14 Perimeter and Area

One should remember that Mathematics is not a spectator sport. It is a valuable tool that can be
used in everyday life, and the more it is applied the more useful it becomes.
Suppose a teacher allocates two projects to all the students of a class: to find the length of the
border to be put around the bulletin board and to find how much carpet is needed for the floor of
the music room of the school. Do you know what is to be determined in the above two projects?
Is it perimeter in the first project and area in the second project?
In the previous class, we have studied about perimeters and areas of some plane figures including
squares and rectangles. In this chapter, we will learn about perimeter and area of some more plane
figures such as triangles, parallelograms, trapeziums and rhombuses. We will also learn how to
find area and circumference of a circle.

Squares and Rectangles
Let’s review some definitions and formulas learnt earlier.
Perimeter is the length of the boundary of a closed plane figure. Area b
Perimeter of a rectangle = 2 × (length + breadth) = 2 × (l + b)
Perimeter of a square = 4 (side) = 4 × l l
Area is the surface or region enclosed inside a closed boundary.
Area of a rectangle = length × breadth = l × b
Area of a square = side × side = l × l
Example 1: A rectangular plot is 50 m long and 30 m wide. Find the:
2
(a) area of the plot (b) cost of the plot, if 1 m costs ` 1,000
Solution: (a) Area of rectangle = length × breadth
Length = 50 m
Breadth = 30 m
2
∴ area of rectangular plot = 50 m × 30 m = 1,500 m .
2
(b) Cost of rectangular plot = Cost of 1 m of the plot × area
= ` 1,000 × 1,500 = ` 15,00,000
∴ cost of plot is ` 15,00,000.
Example 2: Find the area of a square park whose perimeter is 220 m.
Solution: Let the side of the park be a.
Perimeter of the square park = 4 × (side) = 4a
Perimeter of the park = 220 m

∴ 4a = 220
⇒ a = 220 ÷ 4 = 55 m
∴ area of the park = side × side = a × a = 55 m × 55 m = 3,025 sq. m.