Calculate Trapezoid Area: Finding Area with Bases 5cm, 3cm and Height h

Trapezoid Area with Variable Height

Shown below is the trapezoid ABCD.

Given in cm:

AB = 5

DC = 3

Height = h

Calculate the area of the trapezoid.

555333hhhAAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the area of the trapezoid
00:03 We will use the formula for calculating trapezoid area
00:07 (Sum of bases(AB+DC) multiplied by height (H)) divided by 2
00:14 We will substitute appropriate values and solve to find the area
00:23 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Shown below is the trapezoid ABCD.

Given in cm:

AB = 5

DC = 3

Height = h

Calculate the area of the trapezoid.

555333hhhAAABBBCCCDDD

2

Step-by-step solution

Let's calculate the area of trapezoid ABCDABCD:

The formula for the area of a trapezoid is:

Area=12×(Base1+Base2)×Height \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}

In this trapezoid, we have:

  • Base1=AB=5\text{Base}_1 = AB = 5 cm
  • Base2=DC=3\text{Base}_2 = DC = 3 cm
  • Height=h\text{Height} = h

Substituting these into the formula, we get:

Area=12×(5+3)×h \text{Area} = \frac{1}{2} \times (5 + 3) \times h

Simplify the calculation:

Area=12×8×h=4h \text{Area} = \frac{1}{2} \times 8 \times h = 4h

Thus, the area of the trapezoid is 4h4h square centimeters.

3

Final Answer

4h 4h

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area = ½ × (sum of parallel bases) × height
  • Calculation: Substitute values: ½ × (5 + 3) × h = 4h
  • Check: Verify units match and expression simplifies correctly ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to divide by 2 in trapezoid formula
    Don't calculate (5 + 3) × h = 8h as final answer! This gives double the actual area because you missed the ½ factor. Always remember the trapezoid formula includes division by 2 to find the average base length.

Practice Quiz

Test your knowledge with interactive questions

Given the following trapezoid:

AAABBBCCCDDD584

Calculate the area of the trapezoid ABCD.

FAQ

Everything you need to know about this question

Why do we add the two bases together first?

+

The trapezoid formula uses the average of the two parallel sides (bases). Adding 5 + 3 = 8, then multiplying by ½ gives us the average base length of 4.

What if the height was a number instead of h?

+

The process is exactly the same! If height was 6 cm, you'd calculate 12×(5+3)×6=24 \frac{1}{2} \times (5 + 3) \times 6 = 24 square cm.

How do I remember which sides are the bases?

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The bases are the two parallel sides of the trapezoid. In this problem, AB and DC are parallel, so they're the bases (5 cm and 3 cm).

Can I use this formula for any trapezoid?

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Yes! The formula Area=12×(b1+b2)×h \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h works for all trapezoids, as long as you identify the parallel sides correctly.

What units should my answer have?

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Since we're finding area, the units are always square units. Here, with measurements in cm, the answer is 4h 4h square centimeters or cm².

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