Trapezoid Area Calculation: Finding Area with Heights 6cm and Parallel Sides 2.5cm and 4cm

Trapezoid Area Formula with Mixed Number Results

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

2.52.52.5444h=6h=6h=6AAABBBCCCDDD

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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'll use the formula for calculating the area of a trapezoid
00:06 (Sum of bases(AB+DC) multiplied by height (H)) divided by 2
00:13 We'll substitute appropriate values and solve to find the area
00:21 6 divided by 2 becomes 3
00:26 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

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

2.52.52.5444h=6h=6h=6AAABBBCCCDDD

2

Step-by-step solution

First, let's remind ourselves of the formula for the area of a trapezoid:

A=(Base + Base) h2 A=\frac{\left(Base\text{ }+\text{ Base}\right)\text{ h}}{2}

We substitute the given values into the formula:

(2.5+4)*6 =
6.5*6=
39/2 =
19.5

3

Final Answer

1912 19\frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area = (b1+b2)×h2 \frac{(b_1 + b_2) \times h}{2} where b₁, b₂ are parallel sides
  • Technique: Add parallel sides first: (2.5 + 4) × 6 ÷ 2 = 19.5
  • Check: Convert to mixed number: 39 ÷ 2 = 19½ cm² ✓

Common Mistakes

Avoid these frequent errors
  • Using non-parallel sides in the formula
    Don't use the slanted sides AD or BC in the area formula = completely wrong answer! Only the parallel sides (top and bottom) count as bases in a trapezoid. Always identify which sides are parallel before applying the formula.

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 only use the parallel sides in the formula?

+

The trapezoid area formula is based on the average of the parallel sides times the height. The slanted sides don't affect the area - only the parallel bases and the perpendicular distance between them matter!

How do I know which sides are parallel?

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Look for sides that are horizontal or run in the same direction. In this problem, AB (top) = 2.5 cm and DC (bottom) = 4 cm are both horizontal, so they're parallel.

Can I leave my answer as a decimal instead of a mixed number?

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Yes! 19.5 cm² and 19½ cm² are exactly the same value. Choose whichever form the question asks for or feels more natural to you.

What if I forgot to divide by 2 at the end?

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You'd get 39 cm² instead of 19.5 cm² - exactly double the correct answer! The ÷2 step is crucial because the formula finds the average of the parallel sides first.

Does it matter which parallel side I call b₁ or b₂?

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Not at all! Since we're adding the parallel sides together, (2.5 + 4) gives the same result as (4 + 2.5). The order doesn't change the final area.

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