This shape is made from a semicircle and a square. The side of the square is 6 cm. Work out the total area of the shape. Give your answer in terms of π.
How to approach this question
1. **Split the shape into two parts:** a square and a semicircle.
2. **Calculate the area of the square:**
The side length is 6 cm.
Area of square = side × side = 6 × 6 = 36 cm².
3. **Calculate the area of the semicircle:**
The diameter of the semicircle is the same as the side of the square, so diameter = 6 cm.
The radius is half the diameter, so radius (r) = 6 ÷ 2 = 3 cm.
The formula for the area of a full circle is πr².
Area of the full circle = π × 3² = 9π cm².
The area of the semicircle is half of this: (9π) / 2 = 4.5π cm².
4. **Add the two areas together:**
Total Area = Area of square + Area of semicircle
Total Area = 36 + 4.5π cm².
Full Answer
36 + 4.5π cm²
The composite shape is made of a square and a semicircle. To find the total area, we calculate the area of each part and add them together.
**Part 1: Area of the Square**
The side length of the square is given as 6 cm.
The formula for the area of a square is side².
Area_square = 6² = 6 × 6 = 36 cm².
**Part 2: Area of the Semicircle**
The straight edge of the semicircle is attached to the side of the square, so the diameter of the semicircle is 6 cm.
The radius (r) is half of the diameter.
r = 6 cm / 2 = 3 cm.
The formula for the area of a full circle is A = πr².
Area_circle = π × (3)² = 9π cm².
A semicircle is half of a circle, so its area is half the area of the full circle.
Area_semicircle = (9π) / 2 = 4.5π cm².
**Part 3: Total Area**
Total Area = Area_square + Area_semicircle
Total Area = 36 + 4.5π cm².
The question asks for the answer in terms of π, so this is the final answer.
Common mistakes
✗ Using the diameter (6 cm) instead of the radius (3 cm) in the area of a circle formula.\n✗ Forgetting to halve the area of the full circle to find the area of the semicircle.\n✗ Calculating the perimeter instead of the area.
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