The figure not drawn to scale. The figure is made up of a square and a rectangle. It has an overall perimeter of 90 cm. The breadth of the rectangle is ³₅ as long as the length of the square. Given that the length of the rectangle is 13 cm, find the area of the whole figure.
Breadth of rectangle = 3 u
Length of square = 5 u
Length of rectangle = 13 

2 x (5 u + 3 u + 13) = 90
2 x (8 u + 13) = 90
16 u + 26 = 90
16 u = 90 - 26 = 64
1 u = 64 ÷ 16 = 4 

Breadth of the rectangle
= 3 u
= 3 x 4
= 12 

Length of the square
= 5 u
= 5 x 4
= 20 

Area of the rectangle
= 13 x 12
= 156 

Area of the square
= 20 x 20
= 400

Area of the figure
= 156 + 400
= 556 cm²

Answer(s): 556 cm²