Trapezoid Area Problem: Finding DC Length Given Area=80 and Height=8

Q: How do I know which sides are the bases in a trapezoid?

The bases are the two parallel sides. In trapezoid ABCD, look at the diagram carefully - AB (top) and DC (bottom) are horizontal and parallel, so these are your bases.

Q: Why is the area formula different from a triangle?

A trapezoid has two parallel bases of different lengths, unlike a triangle with one base. The formula $ \frac{1}{2} \times h \times (b_1 + b_2) $ finds the average of both bases, then multiplies by height.

Q: What if I get a negative answer for the unknown base?

Check your work! Base lengths are always positive. If you get negative, you might have mixed up the known and unknown values or made an algebra error.

Q: Can I solve this without the area formula?

No, you need the trapezoid area formula since that's the only connection between the given information (area, height, one base) and the unknown base length.

Q: How do I solve for DC once I set up the equation?

From 80 = 4(8 + DC), divide both sides by 4: 20 = 8 + DC. Then subtract 8 from both sides: DC = 12.

Trapezoid Area with Unknown Base Length

Given the trapeze in front of you:

Given h=8, AB=8.

Since the area of the trapezoid ABCD is equal to 80.

Find the length of the side DC.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find DC

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

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

00:29 Divide 8 by 2

00:31 Isolate DC

00:47 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

Given the trapeze in front of you:

Given h=8, AB=8.

Since the area of the trapezoid ABCD is equal to 80.

Find the length of the side DC.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = $\frac{1}{2} \times h \times (b_1 + b_2)$ where bases are parallel sides
Technique: Substitute known values: 80 = $\frac{1}{2} \times 8 \times (8 + DC)$
Check: Verify using Area = $\frac{1}{2} \times 8 \times (8 + 12) = 80$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong sides as bases in trapezoid area formula
Don't use adjacent sides like AB and AD as the two bases = wrong calculation! Only parallel sides are bases in a trapezoid. Always identify which sides are parallel (AB and DC) before applying the area 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

How do I know which sides are the bases in a trapezoid?

The bases are the two parallel sides. In trapezoid ABCD, look at the diagram carefully - AB (top) and DC (bottom) are horizontal and parallel, so these are your bases.

Why is the area formula different from a triangle?

A trapezoid has two parallel bases of different lengths, unlike a triangle with one base. The formula $\frac{1}{2} \times h \times (b_1 + b_2)$ finds the average of both bases, then multiplies by height.

What if I get a negative answer for the unknown base?

Check your work! Base lengths are always positive. If you get negative, you might have mixed up the known and unknown values or made an algebra error.

Can I solve this without the area formula?

No, you need the trapezoid area formula since that's the only connection between the given information (area, height, one base) and the unknown base length.

How do I solve for DC once I set up the equation?

From 80 = 4(8 + DC), divide both sides by 4: 20 = 8 + DC. Then subtract 8 from both sides: DC = 12.

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