Mei Ling overlaps a rectangular piece of red card and a circular piece of blue card on a poster. The overlapping part is shaded. The ratio of the area of the rectangle to the area of the circle is 7 : 5. The shaded part is 27 of the area of the rectangle.
- Find the ratio of the shaded area to the unshaded area of the whole figure. Give your answer in the simplest form.
- The unshaded area of the whole figure is 64 cm². Find the area of the circle.
Need a hint?
Let the rectangle be 7 units. Find how many units the shaded overlap is, then take it away from each shape to find the unshaded parts.
Worked answer
- (a) Rectangle = 7 units. Shaded part = 27 of 7 units = 2 units.
- Circle = 5 units, and 2 of these units are shaded, so the circle's unshaded part = 5 − 2 = 3 units.
- Rectangle's unshaded part = 7 − 2 = 5 units.
- Unshaded area of the whole figure = 5 + 3 = 8 units.
- Shaded : unshaded = 2 : 8 = 1 : 4.
- (b) 8 units = 64 cm², so 1 unit = 64 ÷ 8 = 8 cm².
- Circle = 5 units = 5 × 8 = 40 cm².
The mistake this question tests
Simplest form in final fraction answers
Many pupils write 2 : 12 or 2 : 10 by adding the full areas of both shapes (7 + 5). The overlap is counted in both the rectangle and the circle, so it must be taken out of each before finding the unshaded part.
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See the answer →Practise PSLE ratio until the mistakes stop.
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