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The formula for the area of a trapezoid is [tex]$A = \frac{1}{2} \left( b_1 + b_2 \right) h$[/tex].

The height, [tex]h[/tex], of the trapezoid may be expressed as:

1. [tex]2A - b_1 - b_2[/tex]

2. [tex]\frac{2A - b_1}{b_2}[/tex]

3. [tex]\frac{1}{2}A - b_1 - b_2[/tex]

4. [tex]\frac{2A}{b_1 + b_2}[/tex]

Sagot :

GinnyAnsweridn
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]
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