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Circle · semicircle composite figure
P6 · Circles · PSLE Maths
Question
Siti's school garden is in the shape of a stadium: a rectangle with a semicircle attached to each shorter side. The rectangle is 100 m long and 50 m wide. Take π = 3.14. Find the perimeter and area of the garden.
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Hint
Join the two semicircles to make one whole circle. For the perimeter, count only the outside: two straight sides plus the circumference of one circle.
Show the answer and step-by-step explanation
Answer: Perimeter 357 m; Area 6962.5 m²
- Draw the shape — First, understand the shape: the middle is a 100 m by 50 m rectangle, with a semicircle on each end. The diameter of each semicircle is the width of the rectangle, 50 m.
- Make a circle — The two equal semicircles make one whole circle. The diameter of this circle is 50 m, so its radius is 25 m.
- Find perimeter — For the perimeter, count only the outside. There are two straight sides of 100 m, plus the circumference of one circle made by the two semicircles.
- Rectangle area — We can find the area in parts. First, the rectangle: 100 × 50 = 5000 m².
- Circle area — Next, find the area of the whole circle made by the two semicircles. Its radius is 25 m, so the circle area is 3.14 × 25 × 25 = 1962.5 m².
- Add them — Total area = rectangle area + circle area: 5000 + 1962.5 = 6962.5 m². So the perimeter is 357 m, and the area is 6962.5 m². 📌 Key idea: a stadium shape = rectangle + 1 whole circle; perimeter = 2 straight sides + 1 circumference.
Method: The two semicircles make one whole circle. Perimeter = 2 lengths of the rectangle + circumference of one circle; area = area of rectangle + area of one circle.
Practice: 3 similar questions
- Ali draws a stadium-shaped field: the middle rectangle is 60 m long and 20 m wide, with a semicircle attached to each end. Take π = 3.14. Find the perimeter and area.
Answer
182.8 m, 1514 m² — The two semicircles make 1 whole circle. Diameter = 20 m, radius = 10 m. Perimeter = 2 × 60 + 3.14 × 20 = 120 + 62.8 = 182.8 m. Area = 60 × 20 + 3.14 × 10 × 10 = 1200 + 314 = 1514 m².
- Mei Ling designs a sticker in the shape of a rectangle with a semicircle attached to each end. The rectangle is 12 cm long and 8 cm wide. Take π = 3.14. Find the perimeter and area of the sticker.
Answer
49.12 cm, 146.24 cm² — The two semicircles make 1 whole circle. Diameter = 8 cm, radius = 4 cm. Perimeter = 2 × 12 + 3.14 × 8 = 24 + 25.12 = 49.12 cm. Area = 12 × 8 + 3.14 × 4 × 4 = 96 + 50.24 = 146.24 cm².
- Raju's school has a stadium-shaped grass patch of width 30 m and perimeter 154.2 m. Each end is a semicircle. Take π = 3.14. Find the length of the middle rectangle and the area of the grass patch.
Answer
30 m, 1606.5 m² — The two semicircles make 1 circle of diameter 30 m. Circumference = 3.14 × 30 = 94.2 m. Total length of the two straight sides = 154.2 − 94.2 = 60 m, so the length of the rectangle = 60 ÷ 2 = 30 m. Radius = 30 ÷ 2 = 15 m. Area = 30 × 30 + 3.14 × 15 × 15 = 900 + 706.5 = 1606.5 m².
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