PSLE
The figure is made up of three rectangles. A straight line drawn across the rectangles, divides the figure into two parts: shaded and unshaded.

1. The perimeter of the shaded part is 10 cm longer than the perimeter of the unshaded part. What is the length of ef?
2. What is the area of the shaded part?

(a)
Both shaded and unshaded parts share the same slanted line. The horizontal lengths of the shaded and the unshaded parts are equally long.

For the vertical lengths, the shaded part is 10 cm longer than the unshaded part.

Vertical lengths of shaded part
= ef + 1 u + 1 u
= ef + 2 u

Vertical length of unshaded part = ef

2 u = 10

1 u = 10 ÷ 2 = 5

Length of ef
= 4 + 5 + 10 - 5
= 14 cm

(b)
Length of Rectangle A
= 4 + 5 + 10
= 19 cm

Area of Rectangle A
= 19 x 11
= 209 cm²

Length of Rectangle B
= 4 + 5
= 9 cm

Area of Rectangle B
= 9 x 6
= 54 cm²

Area of Rectangle C
= 4 x 3
= 12 cm²

Height of the unshaded triangle
= 11 + 6 + 3
= 20 cm

Area of the unshaded triangle
= ¹₂ x 14 x 20
= 140 cm²

Area of the shaded part
= 209 + 54 + 12 - 140
= 135 cm²

Answer(s): (a) 14 cm; (b) 135 cm²