Trapezoid Area Problem: Finding Side Length Given Area = 12cm²

Trapezoid Area Formula with Height Finding

The area of the trapezoid in the diagram is equal to 12 cm².

What is the length of the side marked in red?

555777

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's find the length of the red side.
00:10 We'll use the area formula for a trapezoid.
00:15 It's the sum of the bases, A B plus D C, times the height, H, divided by 2.
00:22 Here, the red side is the height, H.
00:29 We'll substitute the given values to find the height.
00:44 Next, multiply everything by 2 to get rid of the fraction.
00:53 Let's isolate H on one side.
01:02 Now, we simplify to find H.
01:07 And that's how we solve this problem! Great job!

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 diagram is equal to 12 cm².

What is the length of the side marked in red?

555777

2

Step-by-step solution

The problem requires finding the height of a trapezoid given its area and the lengths of its bases. We'll use the trapezoid area formula to do this:

  • The formula for the area of a trapezoid is A=12×(b1+b2)×h A = \frac{1}{2} \times (b_1 + b_2) \times h .
  • Substituting in the known values: 12=12×(5+7)×h 12 = \frac{1}{2} \times (5 + 7) \times h .
  • Simplify: 12=12×12×h 12 = \frac{1}{2} \times 12 \times h .
  • Further simplification gives: 12=6×h 12 = 6 \times h .
  • Solving for h h , we divide both sides by 6: h=126 h = \frac{12}{6} .
  • Thus, h=2 h = 2 cm.

By comparing this result to the answer choices, we see that the correct answer is 2 cm 2 \, \text{cm} .

Therefore, the length of the side marked in red is 2 cm\textbf{2 cm}.

3

Final Answer

2 2 cm

Key Points to Remember

Essential concepts to master this topic
  • Area Formula: Trapezoid area equals 12×(b1+b2)×h \frac{1}{2} \times (b_1 + b_2) \times h
  • Algebraic Method: Substitute known values: 12=12×(5+7)×h 12 = \frac{1}{2} \times (5 + 7) \times h
  • Verification: Check answer by substituting back: 12×12×2=12 \frac{1}{2} \times 12 \times 2 = 12 ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong base measurements or formula
    Don't confuse the parallel sides (bases) with the slanted sides = wrong area calculation! The formula uses only the two parallel horizontal sides (5 and 7), not the diagonal red line. Always identify which sides are parallel bases before applying the area formula.

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the trapezoid.

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FAQ

Everything you need to know about this question

How do I identify which sides are the bases of a trapezoid?

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The bases are the two parallel sides - they run in the same direction and never meet. In this problem, the horizontal sides with lengths 5 and 7 are the parallel bases.

What is the red line representing in this diagram?

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The red line is the height of the trapezoid - it's the perpendicular distance between the two parallel bases. This is what we need to find!

Can I use the slanted sides in the area formula?

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No! The area formula for trapezoids only uses the parallel bases and height. The slanted sides don't affect the area calculation directly.

Why do we divide by 2 in the trapezoid formula?

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Think of a trapezoid as the average of the two bases multiplied by height. b1+b22 \frac{b_1 + b_2}{2} gives the average base length, then we multiply by height for the area.

How can I check if my height answer makes sense?

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Substitute your height back into the original formula and see if you get the given area of 12 cm². Also, the height should be a positive number that seems reasonable for the trapezoid size.

What if I get a decimal or fraction for the height?

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That's completely normal! Heights can be any positive number. Just make sure to double-check your arithmetic and verify your answer gives the correct area.

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