Question: Help: PDF Ex. 17.5 Video Ex. 17.5
20. Find the area of the shape from problem 24.13.
Dimensions are in cm. Round to 1 d.p.
Instructions: Do not use the 'pi' on your calculator. Use 3.14 for 'pi'.
Select one:
50.8 cm²
89.2 cm²
15.8 cm²
36.2 cm²
Graph shape: top-right, a rectangle-like shape with vertical sides and a curved semicircular indentation across the top; width 7 cm, right side height 10 cm.
1. **Problem Statement:** Find the area of a shape that looks like a rectangle with a semicircular indentation on the top side.
2. **Given Dimensions:**
- Width of the rectangle (and diameter of the semicircle) = $7$ cm
- Height of the rectangle = $10$ cm
3. **Formula for Area:**
- Area of rectangle = width $\times$ height
- Area of semicircle = $\frac{1}{2} \pi r^2$
4. **Calculate the rectangle area:**
$$\text{Area}_{rectangle} = 7 \times 10 = 70 \text{ cm}^2$$
5. **Calculate the radius of the semicircle:**
$$r = \frac{7}{2} = 3.5 \text{ cm}$$
6. **Calculate the area of the semicircle:**
$$\text{Area}_{semicircle} = \frac{1}{2} \times 3.14 \times (3.5)^2 = \frac{1}{2} \times 3.14 \times 12.25$$
$$= \frac{1}{2} \times 38.465 = 19.2325 \text{ cm}^2$$
7. **Calculate the area of the shape:**
Since the semicircle is an indentation (cut out), subtract its area from the rectangle area:
$$\text{Area}_{shape} = 70 - 19.2325 = 50.7675 \text{ cm}^2$$
8. **Round to 1 decimal place:**
$$50.8 \text{ cm}^2$$
**Final answer:** $50.8$ cm²