Rani needs to buy sod to cover his new backyard. His landscape design is graphed, and the yard has corners at (2,20) , (12,20) , (12,5) , and (2,5) . Solve for the area of his yard.(1 point) Responses 80 sq. ft. 80 sq. ft. 60 sq. ft. 60 sq. ft. 46 sq. ft. 46 sq. ft. 150 sq. ft. 150 sq. ft.

Answer 1

To find the area of Rani's backyard, we can use the coordinates of the corners of the yard to calculate the area of the rectangle formed by those points.

The corner points are:

• (2, 20)
• (12, 20)
• (12, 5)
• (2, 5)

We can see that:

1. The length of the yard (horizontal side) is the distance between (2, 20) and (12, 20): \[ \text{Length} = 12 - 2 = 10 \text{ ft} \]

2. The width of the yard (vertical side) is the distance between (2, 5) and (2, 20): \[ \text{Width} = 20 - 5 = 15 \text{ ft} \]

Now, we can calculate the area using the formula for the area of a rectangle: \[ \text{Area} = \text{Length} \times \text{Width} = 10 \text{ ft} \times 15 \text{ ft} = 150 \text{ sq. ft} \]

Thus, the area of Rani's yard is 150 sq. ft.