What is the area of the polygon? Assume that segments that appear congruent are congruent. The side lengths are 5 and 7.
(1 point)
Multiple choice answers: 190 square units, 140 square units, 76 square units, and 165 square units.
To find the area of the polygon, we need to know the height of the polygon. Given that the side lengths are 5 and 7, we can construct a right triangle with legs of length 5 and 7. Using the Pythagorean theorem, we can find the height of the polygon:
a^2 + b^2 = c^2
5^2 + 7^2 = h^2
25 + 49 = h^2
74 = h^2
h ≈ 8.6
The base of the polygon is 7 units and the height is approximately 8.6 units. Therefore, the area of the polygon is:
Area = (base x height)/2
Area = (7 x 8.6)/2
Area ≈ 30.8 square units
Therefore, the closest answer choice is 76 square units.