Question

A cross-shaped pattern is made by arranging four identical rectangles around the side of a square, as shown in the diagram.

The area of the square is 36cm^2.
The area of each rectangle is one and a third times the area of the square.
Find the perimeter of the cross-shaped pattern.
Show your working and state the units of your answer.

Awarding 15 points. Please someone answer correctly quick, much appreciated x

Answer 1

88 cm

Explanation:

The side of the square = 6 cm, so the shorter side of each rectangle = 6 cms.

The area of each rectangle = 36 * 1 1/3

= 36 * 4/3 = 48 cm^2

So the longer side of each rectangle = 48 / 6 = 8 cms

Therefore, the perimeter of the whole figure

= 4( shorter sides ) + 8(longer sides)

= 4*6 + 8*8

= 24 + 64

= 88 cm (answer)