Question

find the area of the figure below, composed of a parallelogram and one semicircle. rounded to the nearest tenths place

Explanation:

Step1: Calculate area of parallelogram

The formula for the area of a parallelogram is \( A = base \times height \). Here, the base is 18 and the height is 11. So, \( A_{parallelogram} = 18 \times 11 = 198 \).

Step2: Calculate area of semicircle

The diameter of the semicircle is equal to the side of the parallelogram, which is 11? Wait, no, looking at the diagram, the dashed line is 11, so the diameter of the semicircle is 11? Wait, no, maybe the height of the parallelogram is 11, and the diameter of the semicircle is 11? Wait, no, the formula for the area of a semicircle is \( \frac{1}{2} \pi r^2 \), where \( r \) is the radius. If the diameter is 11, then the radius \( r = \frac{11}{2} = 5.5 \). So, \( A_{semicircle} = \frac{1}{2} \pi (5.5)^2 \). Let's calculate that: \( (5.5)^2 = 30.25 \), so \( \frac{1}{2} \pi \times 30.25 = 15.125 \pi \approx 15.125 \times 3.1416 \approx 47.5169 \).

Step3: Total area

Add the area of the parallelogram and the semicircle: \( 198 + 47.5169 \approx 245.5169 \), rounded to the nearest tenths place is 245.5. Wait, wait, maybe I made a mistake in the diameter. Wait, the dashed line is 11, which is the height of the parallelogram, and the semicircle is attached to the side. Wait, maybe the diameter is 11? Wait, no, maybe the side of the parallelogram is 11? Wait, no, the base is 18, height is 11. Wait, the semicircle: let's check again. The diagram shows a parallelogram with base 18, height 11, and a semicircle attached to one side. The diameter of the semicircle should be equal to the length of the side, which is 11? Wait, no, maybe the height is 11, and the diameter is 11. Wait, let's recalculate the semicircle area. \( r = 11/2 = 5.5 \), so \( A_{semicircle} = 0.5 \times \pi \times (5.5)^2 = 0.5 \times \pi \times 30.25 = 15.125 \pi \approx 47.5169 \). Then total area is 18*11 + 15.125π = 198 + 47.5169 ≈ 245.5169, which rounds to 245.5. Wait, but maybe the diameter is 11? Wait, no, maybe I messed up. Wait, another way: maybe the height of the parallelogram is 11, and the diameter of the semicircle is 11. So radius is 5.5. So that's correct. So total area is 198 + 47.5169 ≈ 245.5.

Answer:

245.5