Use the image to answer the question.

A trapezoid, a square, and a semicircle are drawn connected.

Which of the following correctly calculates the area of the figure, rounded to the nearest hundredth? Use π=3.14 .

(1 point)
Responses

19.53 in.2
19.53 in. squared

26.53 in.2
26.53 in. squared

23.07 in.2
23.07 in. squared

16.53 in.2

1 answer

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:

  1. Area of the trapezoid: \[ A_t = \frac{1}{2} \times (b_1 + b_2) \times h_t \]

  2. Area of the square: \[ A_s = s^2 \]

  3. 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.