Question

Find the value of x such that the trapezoid has an area of 52

Answer 1

Consider the following trapezoid

The formula to find the area of this trapezoid is given by the formula

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

In this case, we have h=8, b=x and B=10. So the formula for our trapezoid is given by

$A=\frac{8\cdot(x+10)}{2}=4\cdot(x+10)$

We are told that the area should be 52, so we end up with the following equation

$4\cdot(x+10)=52$

now, we should solve this equation for x. To do so, we start by dividing by 4 on both sides. So we get

$x+10=\frac{52}{4}=\frac{26\cdot2}{2\cdot2}=\frac{26}{2}=13$

Now, we subtract 10 on both sides, so we get

$x=13-10=3$