A garden bed is formed by joining a quarter circle and a semicircle. The quarter circle has centre O and radius 14 cm, with arc PQ and radius OP. The semicircle has its diameter along the straight edge OQ, so its diameter is 14 cm, and it lies outside the quarter circle. Take π = 227. Find the perimeter of the garden bed.
- 36 cm
- 58 cm
- 72 cm
- 80 cm
Need a hint?
List every curved and straight edge on the outside of the figure. OQ is where the two shapes meet, so it is not on the outside.
Worked answer
- Arc PQ of the quarter circle = 14 × 2 × 227 × 14 = 22 cm.
- Straight edge OP is a radius, so OP = 14 cm.
- Semicircle arc on diameter 14 cm = 12 × 227 × 14 = 22 cm.
- The shared edge OQ is hidden inside the figure, so it is not counted.
- Perimeter = 22 + 14 + 22 = 58 cm.
The mistake this question tests
Area and perimeter formulas
Pupils often leave out the semicircle's curved edge, or add OQ, which is the shared edge and is not part of the outline.
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