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Triangle and Circle Areas
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Triangle and Circle Areas
Use π = 3.14 unless a question asks for an exact answer. Show your working and include appropriate units.
Dance showcase set design
Zoe, Hana and Rawiri are planning floor graphics for a dance competition. Calculate carefully so the designs fit their marked spaces.
1.The stage has a circular dance zone with radius 3 m. Which calculation gives its area?
- 3.14 × 3 = 9.42 m²
- 3.14 × 3² = 28.26 m²
- 2 × 3.14 × 3 = 18.84 m²
2.A triangular floor graphic has base 8 m and perpendicular height 5 m. Calculate its area.
3.A round spotlight mat has diameter 6 m. Work out its area to one decimal place. Remember to find the radius first.
4.The semicircular end of a prop has diameter 6 m. Find its area to one decimal place.
Check, compare and design
Use the formulas to solve the remaining design challenges.
5.Zoe says that doubling a circle’s radius doubles its area. Is she correct? Choose the best explanation.
- Yes. Both radius and area double.
- No. The area becomes four times as large because the radius is squared.
- No. The area stays the same because the circle’s shape is unchanged.
6.A circle has diameter 2.5 m. Calculate its area to two decimal places.
7.A triangular banner has area 30 m² and base 10 m. What is its perpendicular height?
8.A spotlight design is made from a triangle with base 6 m and height 4 m joined to a semicircle with diameter 6 m. They meet along the triangle’s base, so the areas do not overlap. Find the total area to one decimal place.
9.Hana claims that a triangle’s height is always one of its sloping sides. Write true or false and explain what height means in an area calculation.
10.Rawiri needs a circular decal with area about 50.24 cm². Using π = 3.14, find its radius and diameter.
11.In one sentence, explain why area is measured in square units, such as m² or cm².
3 printable pages
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