A pentagon can be divided into five congruent triangles as shown. The function y = 5 models the height of each triangleWhat is the area of the pentagon if theta = 54 deg Round to the nearest square foot 10 feet (1 point) 9n ^ 2; 86pi ^ 2; 170n ^ 2; 344pi ^ 2
To find the area of the pentagon, we need to first find the area of one of the congruent triangles.
Since the height of each triangle is 5 and the angle theta is 54 degrees, we can use trigonometry to find the base of the triangle. Since we have a right triangle formed by the height, the base, and the hypotenuse of each triangle, we can use the equation:
tan(54 degrees) = base / 5
base = 5 * tan(54 degrees)
base ≈ 5 * 1.37638
base ≈ 6.88
The area of each triangle is given by the formula: (1/2) * base * height
Area = (1/2) * 6.88 * 5
Area = 17.2 square feet
Since the pentagon is made up of 5 congruent triangles, the area of the pentagon is:
5 * 17.2 = 86 square feet
Therefore, the answer is 86pi ^ 2.