Question

question
find the area of the figure below, composed of an isosceles trapezoid and one semicircle. rounded to the nearest tenths place
answer attempt 1 out of 2

Explanation:

Step1: Calculate Area of Trapezoid

The formula for the area of a trapezoid is $A_{trapezoid} = \frac{(a + b)}{2} \times h$, where $a = 8$, $b = 11$, and $h = 10$.
Substituting values: $A_{trapezoid} = \frac{(8 + 11)}{2} \times 10 = \frac{19}{2} \times 10 = 95$.

Step2: Calculate Area of Semicircle

The diameter of the semicircle is $8$, so radius $r = \frac{8}{2} = 4$.
The formula for the area of a full circle is $A_{circle} = \pi r^2$, so the area of a semicircle is $A_{semicircle} = \frac{1}{2} \pi r^2$.
Substituting $r = 4$: $A_{semicircle} = \frac{1}{2} \pi (4)^2 = \frac{1}{2} \pi \times 16 = 8\pi \approx 25.1327$.

Step3: Total Area

Add the area of the trapezoid and the semicircle: $A_{total} = 95 + 8\pi \approx 95 + 25.1327 = 120.1327$.
Round to the nearest tenths: $120.1$.

Answer:

120.1