Calculate Trapezoid Area: Shape with Bases 5 and 8 Units, Height 3 Units

Trapezoid Area with Mixed Number Results

Calculate the area of the trapezoid.

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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 if possible
00:03 We will use the formula for calculating the area of a trapezoid
00:07 (Sum of bases) multiplied by height) divided by 2
00:11 We will substitute appropriate values according to the given data and solve to find the area
00:41 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate the area of the trapezoid.

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2

Step-by-step solution

To solve this problem, we'll calculate the area of the trapezoid using the standard formula:

  • Step 1: Identify the given dimensions:
  • Shorter base b1=5 b_1 = 5 .
  • Longer base b2=8 b_2 = 8 .
  • Height h=3 h = 3 .

Step 2: We apply the trapezoid area formula, which is:

A=12×(b1+b2)×h A = \frac{1}{2} \times (b_1 + b_2) \times h .

Step 3: Substitute the given values into the formula:

A=12×(5+8)×3 A = \frac{1}{2} \times (5 + 8) \times 3 .

Step 4: Perform the calculations:

A=12×13×3 A = \frac{1}{2} \times 13 \times 3 .

A=12×39 A = \frac{1}{2} \times 39 .

A=19.5 A = 19.5 or 1912 19 \frac{1}{2} .

The area of the trapezoid is 1912 19 \frac{1}{2} .

3

Final Answer

19 1/2

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area equals half times sum of bases times height
  • Calculation: 12×(5+8)×3=1912 \frac{1}{2} \times (5 + 8) \times 3 = 19\frac{1}{2}
  • Check: Sum bases first: 5 + 8 = 13, then multiply by height and divide by 2 ✓

Common Mistakes

Avoid these frequent errors
  • Adding bases after multiplying by height
    Don't calculate 5 × 3 + 8 × 3 = 39 then divide by 2! This treats each base separately instead of using the trapezoid formula. Always add the bases first: (5 + 8) = 13, then multiply by height and divide by 2.

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

Why do we divide by 2 in the trapezoid formula?

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A trapezoid can be thought of as the average of the two bases times the height. Dividing by 2 gives us that average: b1+b22 \frac{b_1 + b_2}{2} .

Which side is the height in a trapezoid?

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The height is always the perpendicular distance between the two parallel sides (bases). In this problem, it's the vertical line marked as 3 units.

Can I get a decimal instead of a mixed number?

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Yes! 1912 19\frac{1}{2} equals 19.5. Both forms are correct, but check which format your teacher prefers.

What if I can't tell which sides are the bases?

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The bases are the two parallel sides of the trapezoid. In this diagram, they're the horizontal lines labeled 5 and 8 units.

Do I need to worry about the order of the bases?

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No! Since we're adding the bases together, it doesn't matter which one you call b1 b_1 or b2 b_2 . Addition is commutative!

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