Here is a rectangle which has a width of x cm. The length of the rectangle is 8cm 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 90cm. Work out the area of the 8-sided shape.

420 cm²

Step-by-step explanation:

Given the width is x then the length is x + 8 ( 8 longer than width )

Given the perimeter = 90 cm

Sum the lengths of the sides stating at the top left corner and going clockwise

Noting that the indentation small part is 8 - x

x + 8 + x + x + 8 - x + 8 + x + x + 8 + x + x + 8 - x + 8 + x

= 6x + 48

Equating perimeters

6x + 48 = 90 ( subtract 48 from both sides )

6x = 42 ( divide both sides by 6 )

x = 7

Thus width = 7 cm and length = 7 + 8 = 15 cm

The figure is made of 4 rectangles, thus

area = 4 × (7 × 15) = 4 ×105 = 420 cm²