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.

Answer 1

Answer:

88 cm

Step-by-step explanation:

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

The area of the square is 36cm^236cm

2

.

So the side length of the square is,

=\sqrt{36}=6cm=

36

=6cm

The area of each rectangle is 1\dfrac{1}{3}1

3

1

of the area of the square.

So the area of each rectangle is,

=1\dfrac{1}{3}\times 36=\dfrac{4}{3}\times 36=48cm^2=1

3

1

×36=

3

4

×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}\times\text{Breadth}=\text{Area}⇒Length×Breadth=Area

\Rightarrow \text{Length}\times 6=48⇒Length×6=48

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

Then perimeter of the cross pattern figure will be,

=4\times \text{Perimeter of the rectangle}-\text{Perimeter of the square}=4×Perimeter of the rectangle−Perimeter of the square

=4\times 2(8+6)-(4\times 6)=4×2(8+6)−(4×6)

=4\times 2(14)-(24)=4×2(14)−(24)

=4\times 28-24=4×28−24

=88cm=88cm