Calculate Trapezoid Height: Finding AE Given Area 18 cm²

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

Look at the diagram carefully! The parallel bases are the horizontal sides: AB (length 3 cm) and DC (length 6 cm). These are the b₁ and b₂ values in the formula.

Q: Why is AE the height and not one of the slanted sides?

AE is drawn perpendicular to both parallel bases, making it the true height. The slanted sides AD and BC are longer than the height because they're diagonal.

Q: Can I use the trapezoid formula even if the numbers are different?

Absolutely! The formula $ \text{Area} = \frac{b_1 + b_2}{2} \times h $ works for any trapezoid. Just substitute your specific values for the bases and solve for the unknown.

Q: What if I get a decimal answer for the height?

That's perfectly normal! Heights can be whole numbers, fractions, or decimals. Just make sure your final answer makes sense when you check it back in the original formula.

Q: How do I remember the trapezoid area formula?

Think of it as the average of the two bases times the height! $ \frac{b_1 + b_2}{2} $ gives you the average base length, then multiply by height to get the area.

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

00:14 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

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

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

Find AE

2

Step-by-step solution

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 $\mathbf{AE = 4 \, \text{cm}}$ .

3

Final Answer

$4$ cm

Key Points to Remember

Essential concepts to master this topic

Formula: Area = (b₁ + b₂)/2 × h for trapezoids
Method: Substitute known values: 18 = (3 + 6)/2 × h
Check: Verify: (3 + 6)/2 × 4 = 4.5 × 4 = 18 cm² ✓

Common Mistakes

Avoid these frequent errors

Confusing which measurement represents the height
Don't assume any side length is the height without checking = wrong calculation! The height must be perpendicular to the parallel bases, not a slanted side. Always identify AE as the perpendicular distance between the parallel sides AB and DC.

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the trapezoid.

FAQ

Everything you need to know about this question

How do I know which sides are the parallel bases?

+

Look at the diagram carefully! The parallel bases are the horizontal sides: AB (length 3 cm) and DC (length 6 cm). These are the b₁ and b₂ values in the formula.

Why is AE the height and not one of the slanted sides?

+

AE is drawn perpendicular to both parallel bases, making it the true height. The slanted sides AD and BC are longer than the height because they're diagonal.

Can I use the trapezoid formula even if the numbers are different?

+

Absolutely! The formula $\text{Area} = \frac{b_1 + b_2}{2} \times h$ works for any trapezoid. Just substitute your specific values for the bases and solve for the unknown.

What if I get a decimal answer for the height?

+

That's perfectly normal! Heights can be whole numbers, fractions, or decimals. Just make sure your final answer makes sense when you check it back in the original formula.

How do I remember the trapezoid area formula?

+

Think of it as the average of the two bases times the height! $\frac{b_1 + b_2}{2}$ gives you the average base length, then multiply by height to get the area.

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Calculate Trapezoid Height: Finding AE Given Area 18 cm²

Trapezoid Area with Height Calculation

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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

How do I know which sides are the parallel bases?

Why is AE the height and not one of the slanted sides?

Can I use the trapezoid formula even if the numbers are different?

What if I get a decimal answer for the height?

How do I remember the trapezoid area formula?

🌟 Unlock Your Math Potential

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