Answer :
To determine the area of a yard that is in the shape of a trapezoid, we can use the formula for the area of a trapezoid:
[tex]\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \][/tex]
Given the following dimensions:
- Base1 (\( \text{Base}_1 \)) = 75 yards
- Base2 (\( \text{Base}_2 \)) = 95 yards
- Height (\( \text{Height} \)) = 30 yards
We substitute these values into the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times (75 + 95) \times 30 \][/tex]
First, add the lengths of the two bases:
[tex]\[ 75 + 95 = 170 \][/tex]
Next, multiply by the height:
[tex]\[ 170 \times 30 = 5100 \][/tex]
Then, divide by 2:
[tex]\[ \frac{5100}{2} = 2550 \][/tex]
Therefore, the area of the trapezoid-shaped yard is:
[tex]\[ 2550 \, \text{yd}^2 \][/tex]
Among the given choices:
- 225 yd²
- 450 yd²
- 1,386 yd²
- 2,772 yd²
None of these choices directly match 2550 yd²; it appears that there may be an error in the provided choices. However, the correct calculation based on the given dimensions yields an area of 2550 square yards.
[tex]\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \][/tex]
Given the following dimensions:
- Base1 (\( \text{Base}_1 \)) = 75 yards
- Base2 (\( \text{Base}_2 \)) = 95 yards
- Height (\( \text{Height} \)) = 30 yards
We substitute these values into the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times (75 + 95) \times 30 \][/tex]
First, add the lengths of the two bases:
[tex]\[ 75 + 95 = 170 \][/tex]
Next, multiply by the height:
[tex]\[ 170 \times 30 = 5100 \][/tex]
Then, divide by 2:
[tex]\[ \frac{5100}{2} = 2550 \][/tex]
Therefore, the area of the trapezoid-shaped yard is:
[tex]\[ 2550 \, \text{yd}^2 \][/tex]
Among the given choices:
- 225 yd²
- 450 yd²
- 1,386 yd²
- 2,772 yd²
None of these choices directly match 2550 yd²; it appears that there may be an error in the provided choices. However, the correct calculation based on the given dimensions yields an area of 2550 square yards.
