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=(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=(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=(52)/(4)=(26\cdot2)/(2\cdot2)=(26)/(2)=13`

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

`x=13-10=3`