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Circles and area

Ten questions of mixed difficulty, covering Circles and area. Print it, or work through it on screen — the answer key starts on its own page.

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Circles and area

Math 7 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. A triangle has an area of 24 cm² and a base of 8 cm. What is its height?

    1. a) 12 cm
    2. b) 3 cm
    3. c) 6 cm
    4. d) 16 cm

  2. A round garden has a radius of 3 m. A path 1 m wide goes all the way around it. Using π ≈ 3.14, what is the area of the path?

    1. a) 3.14 m²
    2. b) 28.26 m²
    3. c) 50.24 m²
    4. d) 21.98 m²

  3. A bike wheel has a radius of 35 cm. Using π ≈ 3.14, how far does the bike move in one full turn of the wheel?

    1. a) 3846.5 cm
    2. b) 70 cm
    3. c) 219.8 cm
    4. d) 109.9 cm

  4. Using π ≈ 3.14, what is the circumference of a circle with a diameter of 10 cm?

    1. a) 78.5 cm
    2. b) 15.7 cm
    3. c) 62.8 cm
    4. d) 31.4 cm

  5. A circular rug has a diameter of 6 m. Using π ≈ 3.14, what is its area?

    1. a) 28.26 m²
    2. b) 18.84 m²
    3. c) 9.42 m²
    4. d) 113.04 m²

  6. Without a calculator, which is the best estimate of the area of a circle with a radius of 10 m?

    1. a) about 60 m²
    2. b) about 1200 m²
    3. c) about 300 m²
    4. d) about 30 m²

  7. A parallelogram has a base of 12 cm and a height of 5 cm. A triangle has the same area and a base of 10 cm. What is the triangle's height?

    1. a) 12 cm
    2. b) 6 cm
    3. c) 30 cm
    4. d) 5 cm

  8. A triangle has a base of 10 cm and a height of 6 cm. What is its area?

    1. a) 8 cm²
    2. b) 30 cm²
    3. c) 16 cm²
    4. d) 60 cm²

  9. A parallelogram has a base of 9 cm, slanted sides of 5 cm and a height of 4 cm. What is its area?

    1. a) 45 cm²
    2. b) 28 cm²
    3. c) 36 cm²
    4. d) 18 cm²

  10. A circle has a radius of 6 cm. What is its diameter?

    1. a) 3 cm
    2. b) 36 cm
    3. c) 18.84 cm
    4. d) 12 cm

Answer key · Circles and area

Math 7 · maddyhelps.com

  1. c) 6 cm — Area = b × h ÷ 2, so 8 × h ÷ 2 = 24. That means 8 × h = 48, and h = 6 cm. 3 cm divides 24 by 8 and forgets that the triangle is only half of 8 × h.
  2. d) 21.98 m² — The garden and path together make a circle of radius 4 m, with area 3.14 × 16 = 50.24 m², and the garden alone has area 3.14 × 9 = 28.26 m². The path is the difference: 50.24 − 28.26 = 21.98 m². 50.24 m² forgets to take the garden away.
  3. c) 219.8 cm — In one turn the wheel rolls out its whole circumference: 2 × 3.14 × 35 = 219.8 cm. 109.9 cm forgets to double the radius — π × r is only half the way round — and 3846.5 is πr², the wheel's area, not a distance.
  4. d) 31.4 cm — Circumference is π times the diameter: 3.14 × 10 = 31.4 cm. 62.8 cm doubles the 10 as if it were the radius, and 78.5 is the area, πr² with r = 5 — a different measurement, in square units.
  5. a) 28.26 m² — The radius is half the diameter, 3 m, so A = 3.14 × 3 × 3 = 28.26 m². Using 6 m as the radius gives 113.04 m², four times too much, and 18.84 is the circumference, π × 6.
  6. c) about 300 m² — π is a little more than 3, so πr² is about 3 × 10 × 10 = 300 m² (the exact value is about 314 m²). About 60 is the circumference, 2πr, and about 1200 m² squares the diameter instead of the radius.
  7. a) 12 cm — The parallelogram's area is 12 × 5 = 60 cm². The triangle needs 10 × h ÷ 2 = 60, so 10 × h = 120 and h = 12 cm. 6 cm forgets that a triangle's area is half of base × height, and 5 cm assumes the same area means the same height.
  8. b) 30 cm² — A triangle is half of a parallelogram with the same base and height, so its area is b × h ÷ 2 = 10 × 6 ÷ 2 = 30 cm². 60 cm² forgets to halve, and 16 adds the base and height instead of multiplying them.
  9. c) 36 cm² — The area of a parallelogram is base × height, and the height is measured straight up from the base, at a right angle: 9 × 4 = 36 cm². 45 cm² uses the slanted side, which is longer than the height, and 18 cm² halves as if it were a triangle.
  10. d) 12 cm — The diameter goes all the way across through the centre, so it is two radii long: 2 × 6 = 12 cm. 3 cm halves the radius instead of doubling it, and 18.84 cm multiplies by π, which gives half the circumference.