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HELP 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 40 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 12 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 14 yards.
PLEASE HELP
What is the area of the playground?

1,728 square yards
1,264 square yards
864 square yards
800 square yards

1 Answer

2 votes

Answer:

None of the answer choices provided, but the closest option is 800 square yards, so that would be the best choice.

Explanation:

To find the area of the playground, we need to divide it into two triangles and one rectangle.

The rectangle has a length of 12 yards and a width of 20 yards, so its area is:

Area of rectangle = length × width

Area of rectangle = 12 × 20

Area of rectangle = 240 square yards

One of the triangles has a base of 14 yards and a height of 20 yards, so its area is:

Area of triangle 1 = (base × height) / 2

Area of triangle 1 = (14 × 20) / 2

Area of triangle 1 = 140 square yards

The other triangle has a base of 26 yards (40 - 14) and a height of 20 yards, so its area is:

Area of triangle 2 = (base × height) / 2

Area of triangle 2 = (26 × 20) / 2

Area of triangle 2 = 260 square yards

Therefore, the total area of the playground is the sum of the areas of the rectangle and the two triangles:

Total area = Area of rectangle + Area of triangle 1 + Area of triangle 2

Total area = 240 + 140 + 260

Total area = 640 square yards

Therefore, the area of the playground is 640 square yards. None of the answer choices provided matches this result exactly, but the closest option is 800 square yards, so that would be the best choice.

User Mourad BENKDOUR
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