Use the image to answer the 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
76 square units
76 square units
140 square units
140 square units
190 square units
190 square units
165 square units
165 square units
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The area of the letter X can be calculated by finding the area of each rectangle and triangle separately and then adding them all together.
Each rectangle has a length of 7 and a width of 5, so the area of each rectangle is 7 x 5 = 35 square units. Since there are four rectangles in the letter X, the total area from the rectangles is 35 x 4 = 140 square units.
The triangles on each side have a base of 7 and a height of 2.5 (since the total width is 5 and each leg is 2.5), so the area of each triangle is (1/2) x 7 x 2.5 = 8.75 square units. Since there are two triangles in the letter X, the total area from the triangles is 8.75 x 2 = 17.5 square units.
Adding the area from the rectangles and the area from the triangles, we get 140 + 17.5 = 157.5 square units.
Therefore, the correct answer is none of the options provided. The area of the polygon is 157.5 square units.