Units, Area, Perimeter and Circles — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Area = πr².

π × 7² = 153.938… ≈ 154 cm²

Question 2

(a)Arc length = (angle/360) × 2πr.

(60/360) × 2π × 9 = 9.42 cm

Question 3

(a)Sector area = (angle/360) × πr².

(60/360) × π × 9² = 42.4 cm²

Question 4

(a)Area of a trapezium = ½(a+b)h.

½(6+10)(4) = 32 cm²

Question 5

(a)Circumference = 2πr.

2π(5.5) ≈ 34.6 cm (3 s.f.)

Question 6

(a)Perimeter = arc length + 2 radii. Arc length = (θ/360)×2πr.

(90/360)×2π(6) + 2(6) = 9.42 + 12 ≈ 21.4 cm

Question 7

(a)Area in m² = 8×5 = 40 m². Convert to cm² by multiplying by 10 000 (since 1 m² = 10 000 cm²).

40 × 10 000 = 400 000 cm²

Question 8

(a)Area of a parallelogram = base × height.

10 × 6 = 60 cm²

Question 9

(a)Semicircle area = ½πr².

½ × π × 4² ≈ 25.1 cm² (3 s.f.)

Question 10

(a)Subtract the removed rectangle's area from the full rectangle's area.

(8×5) − (3×2) = 40 − 6 = 34 cm²

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