Calculate Height AE in Trapezoid with Area 9x Square Centimeters

Question

The area of the trapezoid in the diagram is $9x$ cm².

Calculate 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

00:16 We'll substitute appropriate values according to the given data and solve for H

00:22 In this case, the height is AE

00:30 We'll multiply by 2 to eliminate the fraction

00:39 We'll isolate AE

00:55 And this is the solution to the question

To solve this problem, we will use the formula for the area of a trapezoid:

$\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$

Here, $\text{Area} = 9x$ cm², $\text{Base}_1 = 2x$ cm, and $\text{Base}_2 = 2.5x$ cm.

Substitute the known values into the formula:

$9x = \frac{1}{2} \times (2x + 2.5x) \times \text{AE}$

$9x = \frac{1}{2} \times 4.5x \times \text{AE}$

Multiply through by 2 to clear the fraction:

$18x = 4.5x \times \text{AE}$

Solve for AE by dividing both sides by $4.5x$ :

$\text{AE} = \frac{18x}{4.5x} = 4$

Thus, the height AE is $\textbf{4 cm}$ .

Therefore, the solution to the problem is $\textbf{4}$ cm.

$4$ cm