Calculate Trapezoid Area: Finding Space Between 6cm and 10cm Bases

Trapezoid Area with Parallel Base Measurements

The trapezoid ABCD is shown below.

Base AB = 6 cm

Base DC = 10 cm

Height (h) = 5 cm

Calculate the area of the trapezoid.

666101010h=5h=5h=5AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:10 Let's calculate the area of the trapezoid.
00:13 We'll use the trapezoid area formula.
00:16 The formula is: the sum of base A B and base D C, multiplied by the height, H, and then divided by two.
00:26 Now, let's put in the values and solve for the area.
00:37 And that's how we find the area of a trapezoid!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The trapezoid ABCD is shown below.

Base AB = 6 cm

Base DC = 10 cm

Height (h) = 5 cm

Calculate the area of the trapezoid.

666101010h=5h=5h=5AAABBBCCCDDD

2

Step-by-step solution

First, we need to remind ourselves of how to work out the area of a trapezoid:

(Base+Base)h2=Area \frac{(Base+Base)\cdot h}{2}=Area

Now let's substitute the given data into the formula:

(10+6)*5 =
2

Let's start with the upper part of the equation:

16*5 = 80

80/2 = 40

3

Final Answer

40 cm²

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area equals sum of parallel bases times height divided by two
  • Technique: Add bases first: (6 + 10) = 16, then multiply by height 5
  • Check: Verify units are consistent and answer makes geometric sense: 40 cm² ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying bases instead of adding them
    Don't calculate 6 × 10 × 5 ÷ 2 = 150 cm²! This treats it like a rectangle formula and ignores the trapezoid's slanted sides. Always add the parallel bases first: (6 + 10) × 5 ÷ 2.

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 bases instead of multiplying them?

+

A trapezoid is like the average of two rectangles! Adding the bases and dividing by 2 gives us the average base length, which we then multiply by height to get the area.

What if the trapezoid is upside down or sideways?

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The formula works the same way! Just identify the two parallel sides (they're always the bases) and the perpendicular distance between them (that's your height).

How do I remember the trapezoid area formula?

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Think "Average Base Times Height": (b1+b2)×h2 \frac{(b_1 + b_2) \times h}{2} . The average of the two bases, multiplied by the height!

Can I use this formula for rectangles and parallelograms?

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Yes! A rectangle is just a trapezoid where both bases are equal length. Try it: (6+6)×52=602=30 \frac{(6 + 6) \times 5}{2} = \frac{60}{2} = 30 cm², same as length × width!

What if I don't know the height but know the side lengths?

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You need the perpendicular height, not the slanted side length. If you only have side lengths, you'll need to use trigonometry or coordinate geometry to find the height first.

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