Question

Here is a rectangle.



The length of the rectangle is 7 cm longer than the width of the rectangle.

4 of these rectangles are used to make this 8-sided shape.



The perimeter of the 8-sided shape is 70 cm.

Work out the area of the 8-sided shape.

Answer 1

Given,

Let width of the rectangle be x.

width = x cm

length = x + 7 cm

Perimeter of 8 side shape = 70 cm

To find,

Area of the 8 side shape

Solution,

Perimeter = Addition of all the sides

∵ Perimeter of the 8 sided figure = 8x + 42

8x + 42 = 70

8x = 28

x = 3.5 cm

Therefore,

x + 7 = 3.5 + 7 cm = 10.5 cm

Area of Rectangle = length × breadth

Area = 3.5 × 10.5

Area = 36.75 cm

Since 4 rectangles are used to make the 8 side shape,

Area of 8 side shape = 4 × Area of rectangle

Area of 8 side shape = 4 × 36.75 cm

Area of 8 side shape = 147 cm

Hence, area of the 8 side shape is 147 cm.