Question

The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.

A= 1/2 h(a+b)

Solve for h.

A)h=2(a+b)/A

B)h=a+b/2A

C)h=2A/a+b

D)h=A/2(a+b)

Answer 1

Hey there QueenDobby!

The answer should be C) h = 2A/a+b
To solve for h from the given equation A = $\frac{1}{2}$ h (a+b) we need to isolate h and to do so, we need to start from the parenthesis according to PEMDAS.
So, since $\frac{1}{2}$h it's being multiplied by (a+b), we need to divide (a+b) from both sides and we are left with $\frac{A}{a+b}$ =  $\frac{1}{2}$ h. Now, to isolate h, you can see that h is being multiplied by $\frac{1}{2}$ so what we need to do is to divide $\frac{1}{2}$ from both sides, and when you are dividing fractions, you multiply it by the reciprocal of the fraction.
Example $\frac{a}{b}$ goes to $\frac{b}{a}$
So, the reciprocal leaves us with $\frac{2}{1}$ which is the same as 2. So we multiply both sides by 2 and we are left with h = $\frac{2A}{a+b}$

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