Question

The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h. A=1/2h(a+b) .Solve for b

Answer 1

Answer:

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

Step-by-step explanation:

Solving for a specific variable in a formula requires algebra. The formula for area of trapezoid is given as:

$A=\frac{1}{2}h(a+b)$

We can write this as:

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

We can multiply the "2" with A to get:

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

Now we use "distributive property" on the right side of the equation to get [note: distributive property is  a(b+c) = ab + ac ]:

$2A=ha+hb$

Since we want to solve for b, we keep this term to one side and take others to another and use algebra to come up with an expression for b:

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

This is solving for b, or the expression for b.