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.

Answer 1

The perimeter of the polygon is 110 feet and the area is 360 square feet.

Step-by-step explanation:

The polygon consists of a rectangle and a right triangle. To find the perimeter, we add the lengths of all sides. The length of the rectangle is 20 feet and its width is 15 feet, so the perimeter of the rectangle is 2 * (20 + 15) = 70 feet. The length of the base of the right triangle is 8 feet and the hypotenuse is 17 feet. The other side of the triangle is the height, which is given as 15 feet. Therefore, the perimeter of the polygon is 70 + 8 + 15 + 17 = 110 feet.

To find the area, we calculate the area of the rectangle and the triangle separately and then add them together. The area of the rectangle is length * width = 20 * 15 = 300 square feet. The area of the right triangle is 0.5 * base * height = 0.5 * 8 * 15 = 60 square feet. Therefore, the area of the polygon is 300 + 60 = 360 square feet.

Answer 2

Perimeter =110 feet

Area=360 feet^2

Step-by-step explanation:

Firstly, we can draw diagram

Perimeter:

we will find perimeter of rectangle and right angled triangle

and then we can add them to find perimeter

Perimeter of rectangle = 15+20+15+20

Perimeter of rectangle = 70

Perimeter of triangle = 17+8+15

Perimeter of triangle = 40

so,

total perimeter = (Perimeter of rectangle)+(Perimeter of triangle)

total perimeter =70+40

total perimeter =110 feet

Area:

We can find area of rectangle and area of right angled triangle

and then we can combine them

Area of rectangle is

`=20* 15`

`=300`

Area of triangle is

`=(1)/(2)* 8* 15`

`=60`

now, we can combine

total area =300+60

total area =360 ft^2