Trapezoid Problem: Find Side AB Given Area 126 and Height 9

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

A trapezoid is like the average of two rectangles! The formula $ \frac{(b_1 + b_2) \times h}{2} $ finds the average base length, then multiplies by height.

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

The parallel sides are the bases. In this problem, AB and DC are horizontal and parallel, so they're our bases. The height is always perpendicular to these bases.

Q: What if I get a different equation setup?

That's okay! You might write $ 126 = \frac{9(AB + 15)}{2} $ or $ 252 = 9(AB + 15) $. All lead to the same answer when solved correctly.

Q: Can I solve this without using algebra?

You could try guess and check, but algebra is much faster! Try different values for AB until $ \frac{(AB + 15) \times 9}{2} = 126 $, but solving algebraically saves time.

Q: How do I check if my answer makes sense?

Ask yourself: Is AB = 13 reasonable? Since DC = 15, having AB = 13 makes sense for a trapezoid. Always substitute back to verify your math too!

Trapezoid Area Formula with Unknown Base

Given the trapezoid in front of you:

Given h=9, DC=15.

Since the area of the trapezoid ABCD is equal to 126.

Find the length of the side AB.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find AB

00:03 Use the formula for calculating trapezoid area

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

00:12 Substitute appropriate values and solve for AB

00:20 Multiply by 2 to eliminate the fraction

00:26 Open parentheses properly - multiply each term by 9

00:36 Isolate AB

00:56 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the trapezoid in front of you:

Given h=9, DC=15.

Since the area of the trapezoid ABCD is equal to 126.

Find the length of the side AB.

Step-by-step solution

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

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

We input the data we are given:

$126=\frac{(AB+15)\times9}{2}$

We multiply the equation by 2:

$252=9AB+135$

$252-135=9AB$

$117=9AB$

We divide the two sections by 9

$13=AB$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = (base₁ + base₂) × height ÷ 2
Technique: Substitute known values: 126 = (AB + 15) × 9 ÷ 2
Check: Verify AB = 13: (13 + 15) × 9 ÷ 2 = 126 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by 2 in the area formula
Don't use Area = (base₁ + base₂) × height = wrong result! This gives double the actual area because you forgot the trapezoid formula divides by 2. Always remember the complete formula: Area = (base₁ + base₂) × height ÷ 2.

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 do we divide by 2 in the trapezoid area formula?

A trapezoid is like the average of two rectangles! The formula $\frac{(b_1 + b_2) \times h}{2}$ finds the average base length, then multiplies by height.

How do I know which sides are the parallel bases?

The parallel sides are the bases. In this problem, AB and DC are horizontal and parallel, so they're our bases. The height is always perpendicular to these bases.

What if I get a different equation setup?

That's okay! You might write $126 = \frac{9(AB + 15)}{2}$ or $252 = 9(AB + 15)$ . All lead to the same answer when solved correctly.

Can I solve this without using algebra?

You could try guess and check, but algebra is much faster! Try different values for AB until $\frac{(AB + 15) \times 9}{2} = 126$ , but solving algebraically saves time.

How do I check if my answer makes sense?

Ask yourself: Is AB = 13 reasonable? Since DC = 15, having AB = 13 makes sense for a trapezoid. Always substitute back to verify your math too!

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