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.
- The perimeter of the shaded part is 10 cm longer than the perimeter of the unshaded part. What is the length of st?
- 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
= st + 1 u + 1 u
= st + 2 u
Vertical length of unshaded part = st
2 u = 10
1 u = 10 ÷ 2 = 5
Length of st
= 5 + 6 + 10 - 5
= 16 cm
(b)
Length of Rectangle A
= 5 + 6 + 10
= 21 cm
Area of Rectangle A
= 21 x 13
= 273 cm
2 Length of Rectangle B
= 5 + 6
= 11 cm
Area of Rectangle B
= 11 x 7
= 77 cm
2 Area of Rectangle C
= 5 x 4
= 20 cm
2
Height of the unshaded triangle
= 13 + 7 + 4
= 24 cm
Area of the unshaded triangle
=
12 x 16 x 24
= 192 cm
2
Area of the shaded part
= 273 + 77 + 20 - 192
= 178 cm
2 Answer(s): (a) 16 cm; (b) 178 cm
2