Calculate Trapezoid Area: Finding Area with Height 4 and Parallel Sides 6.5 and 10

Q: Why do I need to add both parallel sides together?

A trapezoid has two different parallel sides (called bases). The formula averages these by adding them and dividing by 2, then multiplies by height. This gives the true area!

Q: Which sides are the parallel ones in this trapezoid?

The parallel sides are the top side (6.5 cm) and the bottom side (10 cm). These are horizontal and never meet, unlike the slanted sides.

Q: What if I forget to divide by 2 in the formula?

You'll get double the correct area! The $ \frac{1}{2} $ is crucial because it finds the average of the two parallel sides. Without it, 16.5 × 4 = 66, but the real answer is 33.

Q: Can I use this formula for rectangles too?

Yes! A rectangle is just a special trapezoid where both parallel sides are equal. So $ \frac{1}{2}(b + b)h = bh $, which is the rectangle formula.

Q: How do I identify the height in a trapezoid?

The height is always the perpendicular distance between the parallel sides. In this problem, it's the vertical line segment labeled 4 cm.

Q: What units should my final answer have?

Since we're calculating area, the units are always square units. Here, length is in cm, so area is in cm² (square centimeters).

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

00:07 (Sum of bases(AB+DC) multiplied by height(H))divided by 2

00:14 We'll substitute appropriate values according to the given data and solve to find the area

00:19 In this case, the height is AE

00:33 Divide 4 by 2

00:48 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

What is the area of the trapezoid in the figure?

2

Step-by-step solution

To solve this problem, we'll compute the area of the trapezoid using the given dimensions and the area formula:

Step 1: Identify the given dimensions:

Base $b_1 = 10$ cm
Base $b_2 = 6.5$ cm
Height $h = 4$ cm

Step 2: Use the trapezoid area formula:

The formula for the area of a trapezoid is $A = \frac{1}{2}(b_1 + b_2)h$ .

Step 3: Substitute the given values into the formula:

$A = \frac{1}{2}(10 + 6.5) \times 4$

Step 4: Calculate the area:

First, calculate the sum of the bases: $10 + 6.5 = 16.5$ .

Next, multiply by the height: $16.5 \times 4 = 66$ .

Finally, divide by 2 to get the area: $\frac{66}{2} = 33$ cm².

Therefore, the area of the trapezoid is $33$ cm².

3

Final Answer

$33$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals half times sum of parallel sides times height
Technique: Calculate $\frac{1}{2}(10 + 6.5) \times 4 = 33$ cm²
Check: Sum of bases (16.5) times height (4) divided by 2 equals 33 ✓

Common Mistakes

Avoid these frequent errors

Using wrong trapezoid area formula
Don't use rectangle formula A = length × width = 10 × 4 = 40! This ignores the second parallel side and gives wrong results. Always use $A = \frac{1}{2}(b_1 + b_2)h$ for trapezoids.

Practice Quiz

Test your knowledge with interactive questions

Given the following trapezoid:

Calculate the area of the trapezoid ABCD.

FAQ

Everything you need to know about this question

Why do I need to add both parallel sides together?

+

A trapezoid has two different parallel sides (called bases). The formula averages these by adding them and dividing by 2, then multiplies by height. This gives the true area!

Which sides are the parallel ones in this trapezoid?

+

The parallel sides are the top side (6.5 cm) and the bottom side (10 cm). These are horizontal and never meet, unlike the slanted sides.

What if I forget to divide by 2 in the formula?

+

You'll get double the correct area! The $\frac{1}{2}$ is crucial because it finds the average of the two parallel sides. Without it, 16.5 × 4 = 66, but the real answer is 33.

Can I use this formula for rectangles too?

+

Yes! A rectangle is just a special trapezoid where both parallel sides are equal. So $\frac{1}{2}(b + b)h = bh$ , which is the rectangle formula.

How do I identify the height in a trapezoid?

+

The height is always the perpendicular distance between the parallel sides. In this problem, it's the vertical line segment labeled 4 cm.

What units should my final answer have?

+

Since we're calculating area, the units are always square units. Here, length is in cm, so area is in cm² (square centimeters).

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Calculate Trapezoid Area: Finding Area with Height 4 and Parallel Sides 6.5 and 10

Trapezoid Area with Given Parallel Sides

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to add both parallel sides together?

Which sides are the parallel ones in this trapezoid?

What if I forget to divide by 2 in the formula?

Can I use this formula for rectangles too?

How do I identify the height in a trapezoid?

What units should my final answer have?

🌟 Unlock Your Math Potential

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