Question

NEED HELP. A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.

A polygon with a horizontal top side labeled 50 yards. The left vertical side is 35 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 18 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 20 yards.

What is the area of the playground?

a. 1,750 square yards
b. 1,855 square yards
c. 2,730 square yards
d. 3,710 square yards

Answer 1

c. 2730 square yards

Explanation:

You want the area of the quadrilateral shown in the attachment.

Composite figure

The given figure can be considered to be composed of trapezoid ABCD and triangle ACE. Using the relevant area formulas, we can find the area of each, then add the results together.

Trapezoid

The area is given by ...

A = 1/2(b1 +b2)h

A = 1/2(70 +50)(35) = 2100 . . . . square yards

Triangle

The area is given by ...

A = 1/2bh

A = 1/2(70)(18) = 630 . . . . square yards

Playground

The area of the playground is the sum of the areas of its parts:

playground area = 2100 yd² +630 yd²

playground area = 2730 yd²