Trapezoid Height Calculation: Find h When Area = 30cm² (4cm & 8cm Parallel Sides)

Q: Why do we divide by 2 in the trapezoid area formula?

A trapezoid can be thought of as the average of its two parallel bases multiplied by height. The division by 2 gives us this average: $ \frac{b_1+b_2}{2} $ × h.

Q: What if I get confused about which sides are the parallel bases?

Look for the parallel sides - they never meet even if extended. In this problem, AB = 4 cm and DC = 8 cm are clearly marked as the parallel bases.

Q: Can I solve this equation a different way?

Yes! You can multiply both sides by 2 first: $ 60 = (4+8) \times h $, then divide by 12. Both methods give the same answer: h = 5 cm.

Q: What units should my final answer have?

Since the parallel sides are given in centimeters and area is in cm², your height must also be in centimeters to make the units work out correctly.

Area Formula Application with Given Measurements

The trapezoid ABCD is shown below.

AB = 4 cm

DC = 8 cm

Area of the trapezoid (S) = 30 cm²

Calculate the height of the trapezoid.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the height of the trapezoid

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

00:06 (Sum of bases(AB+DC) multiplied by height (H)) divided by 2

00:13 We'll substitute appropriate values and solve for the height

00:32 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 trapezoid ABCD is shown below.

AB = 4 cm

DC = 8 cm

Area of the trapezoid (S) = 30 cm²

Calculate the height of the trapezoid.

Step-by-step solution

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

We replace the existing data:

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

$30=\frac{(4+8)\times h}{2}$

We multiply the equation by 2:

$60=(4+8)h$

$60=12h$

We divide the two sections by 12:

$\frac{60}{12}=h$

$5=h$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Trapezoid area equals sum of parallel sides times height divided by 2
Technique: Substitute known values: $30=\frac{(4+8)\times h}{2}$
Check: Verify by substituting h=5 back: $\frac{(4+8)\times 5}{2}=30$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by 2 in the area formula
Don't use Area = (base₁ + base₂) × height = wrong answer doubled! This gives 60 instead of 30. Always remember the trapezoid area formula includes division by 2: $A=\frac{(b_1+b_2)\times h}{2}$ .

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the trapezoid.

FAQ

Everything you need to know about this question

Why do we divide by 2 in the trapezoid area formula?

A trapezoid can be thought of as the average of its two parallel bases multiplied by height. The division by 2 gives us this average: $\frac{b_1+b_2}{2}$ × h.

What if I get confused about which sides are the parallel bases?

Look for the parallel sides - they never meet even if extended. In this problem, AB = 4 cm and DC = 8 cm are clearly marked as the parallel bases.

Can I solve this equation a different way?

Yes! You can multiply both sides by 2 first: $60 = (4+8) \times h$ , then divide by 12. Both methods give the same answer: h = 5 cm.

How do I know my height calculation is reasonable?

Check if your answer makes sense! With bases of 4 cm and 8 cm, a height of 5 cm seems reasonable. Very large or very small heights would be suspicious.

What units should my final answer have?

Since the parallel sides are given in centimeters and area is in cm², your height must also be in centimeters to make the units work out correctly.

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