1. **State the problem:** We need to find the total area of a sign made from a semicircle on top of an isosceles triangle. The base of the semicircle and the top side of the triangle is 48 cm, and the height of the triangle is 64 cm. 2. **Identify the shapes and dimensions:** - The base of the triangle (and diameter of the semicircle) is $48$ cm. - The height of the triangle is $64$ cm. 3. **Formulas to use:** - Area of a triangle: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ - Area of a semicircle: $$\text{Area} = \frac{1}{2} \pi r^2$$ where $r$ is the radius. 4. **Calculate the area of the triangle:** $$\text{Area}_{\triangle} = \frac{1}{2} \times 48 \times 64 = 24 \times 64 = 1536 \text{ cm}^2$$ 5. **Calculate the radius of the semicircle:** $$r = \frac{\text{diameter}}{2} = \frac{48}{2} = 24 \text{ cm}$$ 6. **Calculate the area of the semicircle:** $$\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi (24)^2 = \frac{1}{2} \pi \times 576 = 288\pi \text{ cm}^2$$ 7. **Calculate the total area:** $$\text{Total area} = 1536 + 288\pi$$ 8. **Approximate the total area to 1 decimal place:** Using $\pi \approx 3.1416$, $$288 \times 3.1416 = 904.78$$ $$\text{Total area} \approx 1536 + 904.78 = 2440.78 \text{ cm}^2$$ Rounded to 1 decimal place: $$2440.8 \text{ cm}^2$$ **Final answer:** The total area of the sign is approximately $2440.8$ cm$^2$.