To solve for the height [tex]\( h \)[/tex] of the trapezoid, we can use the given formula for the area of a trapezoid:
[tex]\[ A = \frac{1}{2} h \left(b_1 + b_2\right) \][/tex]
We are given:
- The area [tex]\( A = 28 \)[/tex]
- The length of the first base [tex]\( b_1 = 6 \)[/tex]
- The length of the second base [tex]\( b_2 = 8 \)[/tex]
First, substitute the known values into the formula:
[tex]\[ 28 = \frac{1}{2} h \left(6 + 8\right) \][/tex]
Next, simplify the expression inside the parentheses:
[tex]\[ 28 = \frac{1}{2} h \cdot 14 \][/tex]
Multiply both sides of the equation by 2 to eliminate the fraction:
[tex]\[ 28 \cdot 2 = h \cdot 14 \][/tex]
[tex]\[ 56 = h \cdot 14 \][/tex]
Now solve for [tex]\( h \)[/tex] by dividing both sides of the equation by 14:
[tex]\[ h = \frac{56}{14} \][/tex]
[tex]\[ h = 4 \][/tex]
Therefore, the height of the trapezoid is [tex]\( h = 4 \)[/tex]. The correct answer is:
[tex]\[ h = 4 \][/tex]
