To express the height [tex]\( h \)[/tex] of a trapezoid in terms of its area [tex]\( A \)[/tex], and the bases [tex]\( b_1 \)[/tex] and [tex]\( b_2 \)[/tex], we start with the given formula for the area of a trapezoid:
[tex]\[ A = \frac{1}{2} \left(b_1 + b_2\right) h \][/tex]
Our goal is to solve this formula for [tex]\( h \)[/tex]. Here's the step-by-step process:
1. Start with the given formula:
[tex]\[ A = \frac{1}{2} \left(b_1 + b_2\right) h \][/tex]
2. To eliminate the fraction, multiply both sides of the equation by 2:
[tex]\[ 2A = (b_1 + b_2) h \][/tex]
3. To isolate [tex]\( h \)[/tex], divide both sides by [tex]\( (b_1 + b_2) \)[/tex]:
[tex]\[ h = \frac{2A}{b_1 + b_2} \][/tex]
Thus, the height [tex]\( h \)[/tex] of the trapezoid can be expressed as:
[tex]\[ h = \frac{2A}{b_1 + b_2} \][/tex]
This corresponds to option (4) given in the choices. Therefore, the correct expression for the height [tex]\( h \)[/tex] of the trapezoid is:
[tex]\[ \boxed{\frac{2A}{b_1 + b_2}} \][/tex]
