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.


feet, square feet


feet, square feet


feet, square feet


feet, square feet

area ... rect = 20 * 15 ... tri = 1/2 * 8 * 15 ... ft^2

perim ... 20 + 15 + 20 + 8 + 17 ... ft

To find the perimeter of the trapezoid, we need to add up the lengths of all its sides.

First, let's calculate the lengths of the sides of the trapezoid.

The rectangle has two sides that are 20 feet long and two sides that are 15 feet long.

To find the length of the trapezoid's bottom side, we can use the Pythagorean theorem. The base of the right triangle is 8 feet, and the hypotenuse is 17 feet. Let's call the length of the bottom side "b". So, using the Pythagorean theorem:

b^2 + 15^2 = 17^2
b^2 + 225 = 289
b^2 = 289 - 225
b^2 = 64
b = √64
b = 8

Now that we know the length of the bottom side of the trapezoid is 8 feet, we can calculate the perimeter.

The perimeter of the trapezoid is the sum of all its sides.
Perimeter = length of the rectangle's long side + length of the rectangle's short side + length of the trapezoid's bottom side + length of the trapezoid's other side

Perimeter = 20 + 20 + 8 + 15 + 15
Perimeter = 78 feet

Therefore, the perimeter of the trapezoid is 78 feet.

To find the area of the trapezoid, we can divide it into two parts: the rectangle and the right triangle.

First, let's calculate the area of the rectangle.

Area of the rectangle = length × width
Area of the rectangle = 20 × 15
Area of the rectangle = 300 square feet

Next, let's calculate the area of the right triangle.

Area of the triangle = (base × height) / 2
Area of the triangle = (8 × 15) / 2
Area of the triangle = 120 / 2
Area of the triangle = 60 square feet

Finally, let's calculate the total area of the trapezoid.

Area of the trapezoid = Area of the rectangle + Area of the triangle
Area of the trapezoid = 300 + 60
Area of the trapezoid = 360 square feet

Therefore, the area of the trapezoid is 360 square feet.