Question

C an someone show me step by step how to do this and correctly please

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 45 yards. The left vertical side is 20 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 10 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 12 yards.

What is the area of the playground?

900 square yards

855 square yards

1,710 square yards

1,305 square yards

Answer 1

Sure! To find the area of the playground, we can divide it into two triangles and a rectangle.

First, let's find the area of the rectangle. The rectangle has a height of 20 yards and a width of 10 yards + 12 yards = 22 yards. So the area of the rectangle is:

Area of rectangle = height x width
Area of rectangle = 20 yards x 22 yards
Area of rectangle = 440 square yards

Next, let's find the area of the two triangles. The triangle on the left has a base of 20 yards and a height of 45 yards. So the area of the triangle is:

Area of triangle 1 = (1/2) x base x height
Area of triangle 1 = (1/2) x 20 yards x 45 yards
Area of triangle 1 = 450 square yards

The triangle on the right has a base of 12 yards and a height of 20 yards. So the area of the triangle is:

Area of triangle 2 = (1/2) x base x height
Area of triangle 2 = (1/2) x 12 yards x 20 yards
Area of triangle 2 = 120 square yards

Finally, we can add up the areas of the rectangle and the two triangles to get the total area of the playground:

Total area = area of rectangle + area of triangle 1 + area of triangle 2
Total area = 440 square yards + 450 square yards + 120 square yards
Total area = 1,010 square yards

Therefore, the area of the playground is 1,010 square yards.

HOPE THIS HELPS