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
190 square units
190 square units
140 square units
140 square units
76 square units
The area of a polygon can be found by multiplying the perimeter of the polygon by apothem and dividing by 2.
The perimeter of the polygon is 7 + 7 + 5 + 5 + 7 + 7 + 5 + 5 = 48.
The apothem of the polygon can be found by using the Pythagorean theorem, as each leg of the polygon is a right triangle.
Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
5^2 + 7^2 = c^2
25 + 49 = c^2
74 = c^2
c = sqrt(74)
Now, the area of the polygon is:
Area = (perimeter * apothem) / 2
Area = (48 * sqrt(74)) / 2
Area = 48 * sqrt(74) / 2
Area = 24 * sqrt(74)
Area ≈ 140 square units
Therefore, the correct answer is 140 square units.