Question: A sign for an ice cream shop is made from a semicircle and an isosceles triangle, as shown below. What is the total area of the sign? Give your answer to 1 d.p. 48 cm 63 cm position_hint: center Graph shape: a semicircle sits on top of an isosceles triangle, sharing the same 48 cm top edge/diameter; the full sign is centered in the lower middle of the page.

1. **State the problem:** We need to find the total area of a sign composed of a semicircle and an isosceles triangle. The semicircle has a diameter of $48$ cm, and the triangle has a height of $63$ cm with the same base of $48$ cm. 2. **Formulas used:** - Area of a semicircle: $$A_{semi} = \frac{1}{2} \pi r^2$$ where $r$ is the radius. - Area of a triangle: $$A_{tri} = \frac{1}{2} \times base \times height$$ 3. **Calculate the radius of the semicircle:** $$r = \frac{48}{2} = 24 \text{ cm}$$ 4. **Calculate the area of the semicircle:** $$A_{semi} = \frac{1}{2} \pi (24)^2 = \frac{1}{2} \pi 576 = 288\pi$$ 5. **Calculate the area of the triangle:** $$A_{tri} = \frac{1}{2} \times 48 \times 63 = 24 \times 63 = 1512$$ 6. **Calculate the total area:** $$A_{total} = A_{semi} + A_{tri} = 288\pi + 1512$$ 7. **Approximate the total area using $\pi \approx 3.1416$:** $$288 \times 3.1416 = 904.78$$ $$A_{total} \approx 904.78 + 1512 = 2416.78$$ 8. **Round to 1 decimal place:** $$\boxed{2416.8 \text{ cm}^2}$$ This is the total area of the sign to 1 decimal place.