Calculate Height AE in Trapezoid with Area 9x Square Centimeters

Q: Why does the x cancel out when solving for AE?

The variable x appears on both sides of the equation! When you divide 18x by 4.5x, the x's cancel: $ \frac{18x}{4.5x} = \frac{18}{4.5} = 4 $. This gives a numerical answer.

Q: What if the area was just a number instead of 9x?

If the area was 36 cm² instead of 9x cm², you'd get: 36 = ½ × 4.5x × 4, which gives 36 = 9x, so x = 4. The height AE would still be 4 cm!

Q: How do I know which sides are the parallel bases?

In a trapezoid, the parallel sides are the bases. Look at the diagram: the top side (2x) and bottom side (2.5x) are horizontal and parallel, so these are your two bases.

Q: Can I use decimals instead of fractions in the formula?

Absolutely! You can write the area formula as Area = 0.5 × (base₁ + base₂) × height. Just remember that 0.5 × 4.5x = 2.25x, so you get 9x = 2.25x × AE.

Q: What does AE represent in the trapezoid?

AE is the height (or altitude) of the trapezoid. It's the perpendicular distance between the two parallel bases, shown as the vertical line from point A to point E.

Trapezoid Area with Variable Expressions

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

Calculate AE.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Calculate AE.

Step-by-step solution

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.

Final Answer

$4$ cm

Key Points to Remember

Essential concepts to master this topic

Area Formula: Area = ½ × (base₁ + base₂) × height
Technique: Substitute: 9x = ½ × (2x + 2.5x) × AE
Check: Verify: ½ × 4.5x × 4 = 9x ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms in bases
Don't substitute 2x and 2.5x separately = complicated algebra! This leads to messy calculations and errors. Always combine bases first: 2x + 2.5x = 4.5x, then substitute into the formula.

Practice Quiz

Test your knowledge with interactive questions

Given the following trapezoid:

Calculate the area of the trapezoid ABCD.

FAQ

Everything you need to know about this question

Why does the x cancel out when solving for AE?

The variable x appears on both sides of the equation! When you divide 18x by 4.5x, the x's cancel: $\frac{18x}{4.5x} = \frac{18}{4.5} = 4$ . This gives a numerical answer.

What if the area was just a number instead of 9x?

If the area was 36 cm² instead of 9x cm², you'd get: 36 = ½ × 4.5x × 4, which gives 36 = 9x, so x = 4. The height AE would still be 4 cm!

How do I know which sides are the parallel bases?

In a trapezoid, the parallel sides are the bases. Look at the diagram: the top side (2x) and bottom side (2.5x) are horizontal and parallel, so these are your two bases.

Can I use decimals instead of fractions in the formula?

Absolutely! You can write the area formula as Area = 0.5 × (base₁ + base₂) × height. Just remember that 0.5 × 4.5x = 2.25x, so you get 9x = 2.25x × AE.

What does AE represent in the trapezoid?

AE is the height (or altitude) of the trapezoid. It's the perpendicular distance between the two parallel bases, shown as the vertical line from point A to point E.

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Calculate Height AE in Trapezoid with Area 9x Square Centimeters

Trapezoid Area with Variable Expressions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does the x cancel out when solving for AE?

What if the area was just a number instead of 9x?

How do I know which sides are the parallel bases?

Can I use decimals instead of fractions in the formula?

What does AE represent in the trapezoid?

🌟 Unlock Your Math Potential

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