To calculate the area of the composite figure consisting of a trapezoid, a square, and a semicircle, we need to find the area of each shape individually and then sum them up.
Let’s denote:
- \( b_1 \) = base 1 of the trapezoid
- \( b_2 \) = base 2 of the trapezoid
- \( h_t \) = height of the trapezoid
- \( s \) = side length of the square
- \( r \) = radius of the semicircle
The areas can be calculated as follows:
-
Area of the trapezoid: \[ A_t = \frac{1}{2} \times (b_1 + b_2) \times h_t \]
-
Area of the square: \[ A_s = s^2 \]
-
Area of the semicircle: \[ A_{sc} = \frac{1}{2} \times \pi r^2 \]
Now, sum all the areas: \[ A_{total} = A_t + A_s + A_{sc} \]
Since the problem does not supply the dimensions or values for \( b_1 \), \( b_2 \), \( h_t \), \( s \), or \( r \), it's not possible to provide the exact area.
However, given the provided answer choices:
- 19.53 in.²
- 26.53 in.²
- 23.07 in.²
- 16.53 in.²
If you have specific values for the bases, height, side lengths, or radius, please provide them, and I can help calculate the exact area based on those dimensions to pick the correct answer.