A rectangle is made by placing 4 identical squares side by side in a row. Each square has a side of 6 cm. A semicircle with diameter 6 cm is attached to the right-hand short edge of the rectangle, so that the curve replaces that edge. Take π = 3.14.
- Find the length of the curved edge of the semicircle.
- Find the perimeter of the whole figure.
Need a hint?
The curved edge is half of a circle's circumference. The right-hand edge of the rectangle is no longer part of the outline.
Worked answer
- Length of the rectangle = 4 × 6 = 24 cm.
- Diameter of the semicircle = 6 cm, so its radius = 3 cm.
- (a) Curved edge = 12 × 3.14 × 6 = 9.42 cm.
- Straight edges: top 24 cm, bottom 24 cm and left edge 6 cm, so 24 + 24 + 6 = 54 cm.
- The right-hand edge is replaced by the curve, so it is not counted.
- (b) Perimeter = 54 + 9.42 = 63.42 cm.
The mistake this question tests
Radius and diameter in circles
Many pupils use 6 cm as the radius, getting 18.84 cm for the curve and 72.84 cm in all, or they also keep the 6 cm right-hand edge and get 69.42 cm.
How to fix it at home →Wrong answers children often give:
- 72.84 Radius and diameter in circles
- 69.42 Area and perimeter formulas
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