Calculate Trapezoid Height: Finding AE Given Area 18 cm²

Question

The area of the trapezoid in the drawing is equal to 18 cm².

Find AE

00:00 Find AE

00:03 We'll use the formula for calculating trapezoid area

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

00:14 We'll substitute appropriate values according to the given data and solve for height

00:19 In this case the height is AE

00:28 We'll multiply by 2 to eliminate the fraction

00:38 We'll isolate AE

00:48 And this is the solution to the question

To determine the length of side $AE$ , we'll use the formula for the area of a trapezoid. The formula is:

$\text{Area} = \left( \frac{b_1 + b_2}{2} \right) \times h$

Given values are $b_1 = 3$ cm, $b_2 = 6$ cm, and $\text{Area} = 18$ cm $^2$ .

Substituting these into the equation:

$18 = \left( \frac{3 + 6}{2} \right) \times h$

Simplify the expression:

$18 = \left( \frac{9}{2} \right) \times h$

Multiply both sides of the equation by 2 to eliminate the fraction:

$36 = 9h$

Now, solve for $h$ by dividing both sides by 9:

$h = \frac{36}{9} = 4$

Thus, the length of side $AE$ is 4 cm.

Therefore, the solution to the problem is $\mathbf{AE = 4 \, \text{cm}}$ .

$4$ cm