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 6 cm longer than the perimeter of the unshaded part. What is the length of lm?
2. What is the area of the shaded part?

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

For the horizontal lengths, the shaded part is 6 cm longer than the unshaded part.

Horizontal lengths of shaded part
= lm + 1 u + 1 u
= lm + 2 u

Horizontal length of unshaded part = lm

2 u = 6

1 u = 6 ÷ 2 = 3

Length of lm
= 6 + 11 - 3
= 14 cm

(b)
Length of Rectangle A
= 6 + 11
= 17 cm

Area of Rectangle A
= 17 x 10
= 170 cm²

Area of Rectangle B
= 6 x 5
= 30 cm²

Height of the unshaded triangle
= 10 + 5
= 15 cm

Area of the unshaded triangle
= ¹₂ x 14 x 15
= 105 cm²

Area of the shaded part
= 170 + 30 - 105
= 95 cm²

Answer(s): (a) 14 cm; (b) 95 cm²