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 composite figure is made by arranging four identical rectangles around the side of a square.

The area of the square is
`36cm^2`.

So the side length of the square is,

`=√(36)=6cm`

The area of each rectangle is
`1(1)/(3)` of the area of the square.

So the area of each rectangle is,

`=1(1)/(3)* 36=(4)/(3)* 36=48cm^2`

As the breadth of each rectangle is equal to the side length of the square i.e 6 cm, so

`\Rightarrow \text{Length}*\text{Breadth}=\text{Area}`

`\Rightarrow \text{Length}* 6=48`

`\Rightarrow \text{Length}=8cm`

Then perimeter of the cross pattern figure will be,

`=4* \text{Perimeter of the rectangle}-\text{Perimeter of the square}`

`=4* 2(8+6)-(4* 6)`

`=4* 2(14)-(24)`

`=4* 28-24`

`=88cm`