Question: The compound shape below is formed from a semicircle and a rectangle.
Calculate the area of the compound shape.
Give your answer to 1 d.p.
3 cm
16 cm
Graph/shape: A compound green shape is shown in the bottom-center of the page, made of a semicircle on the left attached to a vertical rectangle on the right. The rectangle is 3 cm wide and 16 cm tall, and the semicircle has diameter 16 cm with its curved edge on the left. position_hint: bottom-right
1. **State the problem:** We need to find the area of a compound shape made of a semicircle and a rectangle.
2. **Identify dimensions:** The rectangle has width $3$ cm and height $16$ cm. The semicircle has diameter $16$ cm, so radius $r = \frac{16}{2} = 8$ cm.
3. **Formula for area of rectangle:**
$$\text{Area}_{\text{rectangle}} = \text{width} \times \text{height}$$
4. **Calculate area of rectangle:**
$$\text{Area}_{\text{rectangle}} = 3 \times 16 = 48 \text{ cm}^2$$
5. **Formula for area of semicircle:**
$$\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2$$
6. **Calculate area of semicircle:**
$$\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi (8)^2 = \frac{1}{2} \pi 64 = 32\pi \text{ cm}^2$$
7. **Calculate total area:**
$$\text{Area}_{\text{total}} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{semicircle}} = 48 + 32\pi$$
8. **Approximate using $\pi \approx 3.1416$:**
$$32 \times 3.1416 = 100.53$$
9. **Final total area:**
$$48 + 100.53 = 148.53 \text{ cm}^2$$
10. **Round to 1 decimal place:**
$$148.5 \text{ cm}^2$$
**Answer:** The area of the compound shape is $148.5$ cm$^2$ to 1 decimal place.