Trapezoid Problem: Find Side AB Given Area 126 and Height 9

Question

Given the trapezoid in front of you:

Given h=9, DC=15.

Since the area of the trapezoid ABCD is equal to 126.

Find the length of the side AB.

00:00 Find AB

00:03 Use the formula for calculating trapezoid area

00:07 (Sum of bases(AB+DC) multiplied by height(H)) divided by 2

00:12 Substitute appropriate values and solve for AB

00:20 Multiply by 2 to eliminate the fraction

00:26 Open parentheses properly - multiply each term by 9

00:36 Isolate AB

00:56 And this is the solution to the problem

We use the formula to calculate the area: (base+base) times the height divided by 2

$S=\frac{(AB+CD)\times h}{2}$

We input the data we are given:

$126=\frac{(AB+15)\times9}{2}$

We multiply the equation by 2:

$252=9AB+135$

$252-135=9AB$

$117=9AB$

We divide the two sections by 9

$13=AB$