Trapezoid Area Calculation: Finding Area with Heights 5 and Bases 8 and 13

Trapezoid Formula with Parallel Base Measurements

What is the area of the trapezoid in the diagram?

555138

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's calculate the area of the trapezoid.
00:08 We'll use the area formula for a trapezoid.
00:11 Add both bases, A B, and D C. Multiply by height, H, then divide by two.
00:18 Now, substitute the given values. Solve to find the area.
00:44 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the area of the trapezoid in the diagram?

555138

2

Step-by-step solution

To find the area of the trapezoid, we will follow these steps:

  • Step 1: Identify the given dimensions of the trapezoid.
  • Step 2: Apply the area formula for a trapezoid using these dimensions.
  • Step 3: Perform the calculation to determine the area.

Let's work through each step more clearly:
Step 1: From the problem, we identify that the trapezoid has one base b1=13b_1 = 13 units, another base b2=8b_2 = 8 units, and its height h=5h = 5 units.
Step 2: 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

Step 3: Substitute the values into the formula:

A=12×(13+8)×5 A = \frac{1}{2} \times (13 + 8) \times 5

A=12×21×5 A = \frac{1}{2} \times 21 \times 5

A=12×105 A = \frac{1}{2} \times 105

A=52.5units2 A = 52.5 \, \text{units}^2

Therefore, the area of the trapezoid is 52.5units2 52.5 \, \text{units}^2 .

3

Final Answer

52.5 52.5 cm²

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area = 12×(b1+b2)×h \frac{1}{2} \times (b_1 + b_2) \times h for trapezoids
  • Technique: Add bases first: 13 + 8 = 21, then multiply by height
  • Check: Verify units match and answer seems reasonable for given dimensions ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong base measurements
    Don't confuse the parallel bases with the slanted sides = wrong area calculation! The slanted sides are NOT used in the area formula. Always identify the two parallel horizontal lines as your bases (8 and 13 in this problem).

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

Which lines are the bases in a trapezoid?

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The bases are the two parallel sides - in this diagram, the horizontal lines measuring 8 and 13. The slanted sides are called legs and are not used in the area formula.

Why do we multiply by 1/2 in the trapezoid formula?

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Think of a trapezoid as an average rectangle! The 12 \frac{1}{2} finds the average of the two bases: 8+132=10.5 \frac{8 + 13}{2} = 10.5 , then we multiply by height like a rectangle.

What if the height isn't drawn vertically?

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The height is always the perpendicular distance between the parallel bases. Even if drawn at an angle, it represents the shortest distance between the two parallel lines.

Can I use the formula if the bases are different lengths?

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Yes! That's exactly what makes it a trapezoid. If both bases were the same length, it would be a rectangle or parallelogram instead.

How do I remember the trapezoid area formula?

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Remember: "Average the bases, then multiply by height" - b1+b22×h \frac{b_1 + b_2}{2} \times h is the same as 12×(b1+b2)×h \frac{1}{2} \times (b_1 + b_2) \times h !

Why is my answer 52.5 instead of a whole number?

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Decimal answers are perfectly normal in geometry! Areas don't have to be whole numbers. Always include proper units (like cm² or square units) in your final answer.

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