Rosyth Sch 2006 PSLE Math Prelim Q37

The figure below consists of two overlapping shapes, a square and a triangle. The ratio of the area of the square to the area of the triangle is 2 : 3. 1/8 of the square is shaded. The shaded area in the figure is 15 square cm. Find the area of the unshaded part of the figure.



Solution

Area of square
1/8 area ----- 15 square cm
8/8 area ----- 15 square cm x 8 = 120 square cm

Area of square : Area of triangle
2 : 3

(Square) 2 units ----- 120 square cm
1 unit ----- 120 square cm divided by 2 = 60 square cm
(Triangle) 3 units ----- 3 x 60 square cm = 180 square cm

Unshaded area ----- (Total area of square + total area of triangle - shaded area of the triangle - shaded area square)

(120 + 180 – 15 –15) square cm
= 270 square cm (Answer)