To determine the height of a trapezoid, we can use the formula for the area of a trapezoid, which is given by:
[tex]\[ \text{Area} = \frac{1}{2} \times ( \text{base}_1 + \text{base}_2 ) \times \text{height} \][/tex]
Given:
- The area of the trapezoid, [tex]\( A = 70.55 \)[/tex] square feet
- The lengths of the bases, [tex]\( \text{base}_1 = 11.4 \)[/tex] feet and [tex]\( \text{base}_2 = 5.6 \)[/tex] feet
We need to solve for the height, [tex]\( h \)[/tex]. Rearranging the formula to solve for height:
[tex]\[ \text{height} = \frac{2 \times \text{Area}}{(\text{base}_1 + \text{base}_2)} \][/tex]
Substituting the given values into the formula:
[tex]\[ \text{height} = \frac{2 \times 70.55}{11.4 + 5.6} \][/tex]
First, add the lengths of the bases:
[tex]\[ 11.4 + 5.6 = 17 \][/tex]
Then, multiply the area by 2:
[tex]\[ 2 \times 70.55 = 141.1 \][/tex]
Finally, divide by the sum of the bases:
[tex]\[ \text{height} = \frac{141.1}{17} \approx 8.3 \][/tex]
Therefore, the height of the trapezoid is approximately [tex]\( 8.3 \)[/tex] feet.
So the correct answer is:
[tex]\[ \boxed{8.3 \text{ ft}} \][/tex]
The options related to this:
- [tex]\( 4.15 \text{ ft} \)[/tex]
- [tex]\( 4.15 \text{ ft}^2 \)[/tex]
- [tex]\( 8.3 \text{ ft} \)[/tex]
- [tex]\( 8.3 \text{ ft}^2 \)[/tex]
Among these, the correct option is:
[tex]\[ 8.3 \text{ ft} \][/tex]
