Question

Question
Use the image to answer the question.

An illustration shows the outline of letter upper T. The vertical rectangular base of the letter has length 12 and width 3. The horizontal rectangular crossbar at the top has thickness 2. The lower sides of the horizontal crossbar on either side of the vertical base measure 4.

What is the area of the polygon? Assume that segments that appear congruent are congruent and angles that appear to be right angles are right angles.

(1 point)
Responses

50 square units
50 square units

58 square units
58 square units

52 square units
52 square units

64 square units

Answer 1

To calculate the area of the outlined letter T, we will break it into rectangular parts.

1. **Vertical Rectangle (Base of T)**:
- Length = 12
- Width = 3
- Area (A1) = length × width = 12 × 3 = 36 square units.

2. **Horizontal Rectangle (Crossbar of T)**:
- The width of the horizontal part is equal to the section that extends beyond the vertical base on both sides. Since the vertical base is 3 wide and extends 4 units on either side, the total width of the horizontal crossbar is:
\[
3 + 4 + 4 = 11 \text{ units}
\]
- The thickness of the crossbar is given as 2.
- Area (A2) = width × thickness = 11 × 2 = 22 square units.

3. **Total Area**:
- To find the total area of the polygon, add the areas of both rectangles:
\[
A_{\text{total}} = A1 + A2 = 36 + 22 = 58 \text{ square units}.
\]

Thus, the area of the polygon is **58 square units**.