Question

The formula for the area of a trapezoid is A = ;(b, + b,)h. Solve the formula for h.

Answer 1

Answer:

$\frac{A}{2b} = h$ with your formula but

$\frac{2a}{a+b} = h$ with the formula for the area of a trapezoid.

Step-by-step explanation:

A = (b + b)h

You mentioned that this is the area for a trapezoid, I will answer giving the formula you have provided however I will also include an explanation for the actual area for the trapezoid as the one you provided is inaccurate.

A = (b + b)h

Firstly, add together the two b variables:

A = 2bh

Now, divide both sides by 2b:

$\frac{A}{2b} = \frac{2bh}{2b}$

$\frac{A}{2b} = h$

However, the formula for the area of a trapezoid is:

$A = \frac{a+ b}{2}h$

So to solve for h, first, we must multiply both sides by 2:

$A * 2 = (\frac{a+ b}{2}h) *2 = 2A = h(a+b)$

2A = h(a+b)

Now, divide both sides by (a+b)

$\frac{2a}{(a+b)} = \frac{h(a+b)}{(a+b)}$

Which cancels down to:

$\frac{2a}{a+b} = h$

Hope this helps!