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

`b=(2A)/(h)-a`

Explanation:

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

`A=(1)/(2)h(a+b)`

We can write this as:

`A=(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=(2A-ha)/(h)\\b=(2A)/(h)-(ha)/(h)\\b=(2A)/(h)-a`

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