A square and a rectangle are isoperimetric and have a perimeter of 80 cm. knowing that the height of the rectangle exceeds the bases of 12 cm, calculates the area of each figure.

[364cm2; 400cm2]

Square

(80:4) ² =

20²=

400 cm² (area)

Rectangle

80:2=40cm (b+h)

40-12=28cm

28:2=14cm (b)

14+12=26cm (h)

A = b*h

14*26 = 364 cm² (area)

Each side of the square would be 80/4 = 20 cm. so its area = 20^2 = 400 cm^2.

Th rectangle will have perimeter = 80 = 2x + 2 (x - 12) where x = height of the rectangle

4x = 80+24 = 104

so x = 26

area of rectangle = 26 * (26-12) = 364 cm^2