Answer to Question #285675 in Geometry for wis

Question

One of the bases of the trapezoid is 5 units and the height of it is 12 units. If the area

of the trapezoid is 138 square units, then what is the length of the other base?

Answer 1

Let $a=$ the first base of the trapezoid, $b=$ the second base of the trapezoid,

$h=$ the height of the trapezoid.

Then

$$S=\dfrac{a+b}{2}\cdot h$$

Solve for $b$

$$b=\dfrac{2S}{h}-a$$

Given $a=5units, h=12units, S=138{units}^2.$

Substitute

$$b=\dfrac{2(138)}{12}-5=18(units)$$

The other base of the trapezoid is 18 units.