Use the image to answer the question.

Question

An illustration shows the outline of letter X. The length of each of the four legs is 7, and the width of each is 5.

What is the area of the polygon? Assume that segments that appear congruent are congruent.

(1 point)
Responses

165 square units
165 square units

76 square units
76 square units

190 square units
190 square units

140 square units
140 square units

Answer 1

The area of the polygon is 165 square units.

To find the area, we can divide the polygon into two rectangles and two triangles. The rectangles have dimensions of 5 by 7, so each has an area of 35 square units. The triangles have base 7 and height 2.5 (half of the width of the X), so each has an area of 8.75 square units.

Therefore, the total area is:

2 (35 square units) + 2 (8.75 square units) = 70 square units + 17.5 square units = 87.5 square units

However, since the polygon is symmetric across both diagonals of the X, we know that the total area must be twice this value:

2 (87.5 square units) = 175 square units

So the answer is closest to 165 square units.