Question

Find the perimeter and area of the polygon shown below. the polygon is a trapezoid made up of a rectangle and a right triangle. the rectangle is 20 feet long and 15 feet wide. the right triangle joins the rectangle at a side that is 15 feet wide, and this is the height of the triangle. the base of the triangle is 8 feet and the hypotenuse is 17 feet.

a) Perimeter: 94 feet, Area: 220 square feet
b) Perimeter: 90 feet, Area: 210 square feet
c) Perimeter: 100 feet, Area: 200 square feet
d) Perimeter: 88 feet, Area: 190 square feet

Answer 1

The perimeter of the trapezoid is 100 feet and the area is 360 square feet.

Step-by-step explanation:

To find the perimeter of the trapezoid, we need to calculate the sum of all the sides. The rectangle has two sides of length 20 feet and two sides of length 15 feet, so the perimeter of the rectangle is 20 + 20 + 15 + 15 = 70 feet. The right triangle has a base of 8 feet and a hypotenuse of 17 feet, so we can use the Pythagorean Theorem to find the height of the triangle: height = sqrt(17^2 - 8^2) = sqrt(289 - 64) = 15 feet. Therefore, the perimeter of the trapezoid is 70 + 15 + 15 = 100 feet.

To find the area of the trapezoid, we can calculate the area of the rectangle and the area of the triangle, and then add them together. The area of the rectangle is length times width = 20 * 15 = 300 square feet. The area of the triangle is 1/2 * base * height = 1/2 * 8 * 15 = 60 square feet. Therefore, the total area is 300 + 60 = 360 square feet.