Answer both parts about shaded and unshaded areas. (a) Three identical rectangles are placed side by side to form one large rectangle. A triangle is shaded with its base along the bottom edge of the first two rectangles and its top vertex at the top-right corner of the large rectangle. The area of the shaded triangle is 150 cm². Find the difference in area between the shaded and unshaded parts of the large rectangle. (b) Three identical squares, each with area 100 cm², are placed side by side. Inside each square is a circle that touches all four sides of the square. The three circles are shaded and the rest of the three squares is unshaded. Find the difference in area between the shaded and unshaded parts. (Take π = 3.14)

Area & volumeStructured · 5 marks

Answer both parts about shaded and unshaded areas.

Three identical rectangles are placed side by side to form one large rectangle. A triangle is shaded with its base along the bottom edge of the first two rectangles and its top vertex at the top-right corner of the large rectangle. The area of the shaded triangle is 150 cm². Find the difference in area between the shaded and unshaded parts of the large rectangle.
Three identical squares, each with area 100 cm², are placed side by side. Inside each square is a circle that touches all four sides of the square. The three circles are shaded and the rest of the three squares is unshaded. Find the difference in area between the shaded and unshaded parts. (Take π = 3.14)

Need a hint?

For (a), the triangle's base is two rectangles wide, so compare it with the height of one rectangle. For (b), find the side of each square first, then the radius of each circle.

Worked answer

(a) The triangle's base covers two rectangle widths and its height is one rectangle's height, so its area is one rectangle's area.
(a) So one rectangle is 150 cm², the large rectangle is 450 cm², and the unshaded part is 450 − 150 = 300 cm².
(a) Difference = 300 − 150 = 150 cm².
(b) Each square has side 10 cm (since 10 × 10 = 100), so each circle has radius 5 cm.
(b) Three circles have area 3 × 3.14 × 5 × 5 = 235.5 cm² (shaded).
(b) Unshaded part = 300 − 235.5 = 64.5 cm².
(b) Difference = 235.5 − 64.5 = 171 cm².

Answer: 171 cm²

The mistake this question tests

Habit

Area and perimeter formulas

Pupils often treat the triangle's base as one rectangle width, or use the side length as the radius, or subtract the circles' area from the squares' area and forget to compare the two parts correctly.

How to fix it at home →

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