Calculate Trapezoid Area: Using Bases 4cm, 8cm and Height 6cm

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

A trapezoid is like a triangle with its top cut off. The formula $ \frac{1}{2} \times (b_1 + b_2) \times h $ finds the average of the two bases, then multiplies by height - just like finding the area of a rectangle with the average base length!

Q: Which sides are the bases in a trapezoid?

The bases are the two parallel sides. In this problem, BC (4 cm) and AD (8 cm) are parallel to each other, so they're the bases. The other two sides are called legs.

Q: Does it matter which base I call base₁ and base₂?

No, it doesn't matter! Since we're adding the bases together, 4 + 8 gives the same result as 8 + 4. The trapezoid area formula works regardless of which base you list first.

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

The height is always the perpendicular distance between the parallel bases. Look for a line that forms a right angle (90°) with both bases - that's your height measurement.

Q: What if I get a different answer when I calculate?

Double-check these steps: Add the bases: 4 + 8 = 12Multiply by height: 12 × 6 = 72Multiply by $ \frac{1}{2} $: 72 ÷ 2 = 36 Remember to include square units in your final answer!

Trapezoid Area with Parallel Base Measurements

The trapezoid ABCD is shown below.

The height of ABCD is 6 cm.

The base BC is equal to 4 cm.

The base AD is equal to 8 cm.

Calculate the area of trapezoid ABCD.

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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 Let's use the formula for calculating the area of a trapezoid

00:07 ((sum of bases) times height) divided by 2

00:13 Let's substitute appropriate values according to the given data and solve for the area

00:39 Divide 12 by 2

00:47 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The trapezoid ABCD is shown below.

The height of ABCD is 6 cm.

The base BC is equal to 4 cm.

The base AD is equal to 8 cm.

Calculate the area of trapezoid ABCD.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate formula
Step 3: Perform the necessary calculations

Now, let's work through each step:

Step 1: The problem gives us the height of the trapezoid as $6 \, \text{cm}$ , base BC as $4 \, \text{cm}$ and base AD as $8 \, \text{cm}$ .

Step 2: We'll use the formula for the area of a trapezoid:

$A = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$

Step 3: Substituting the given values into the formula:

$A = \frac{1}{2} \times (4 + 8) \times 6$

Calculating further,

$A = \frac{1}{2} \times 12 \times 6$

$A = \frac{1}{2} \times 72$

$A = 36 \, \text{cm}^2$

Therefore, the area of the trapezoid ABCD is $36 \, \text{cm}^2$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals half times sum of bases times height
Technique: Add bases first: 4 + 8 = 12, then multiply by height
Check: Verify units are squared and calculation: $\frac{1}{2} \times 12 \times 6 = 36$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by one-half in the trapezoid formula
Don't calculate (4 + 8) × 6 = 72 as your final answer! This gives the area of a rectangle, not a trapezoid. Always multiply the entire calculation by $\frac{1}{2}$ to get the correct trapezoid area.

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 we multiply by 1/2 in the trapezoid formula?

A trapezoid is like a triangle with its top cut off. The formula $\frac{1}{2} \times (b_1 + b_2) \times h$ finds the average of the two bases, then multiplies by height - just like finding the area of a rectangle with the average base length!

Which sides are the bases in a trapezoid?

The bases are the two parallel sides. In this problem, BC (4 cm) and AD (8 cm) are parallel to each other, so they're the bases. The other two sides are called legs.

Does it matter which base I call base₁ and base₂?

No, it doesn't matter! Since we're adding the bases together, 4 + 8 gives the same result as 8 + 4. The trapezoid area formula works regardless of which base you list first.

How do I identify the height in a trapezoid diagram?

The height is always the perpendicular distance between the parallel bases. Look for a line that forms a right angle (90°) with both bases - that's your height measurement.

What if I get a different answer when I calculate?

Double-check these steps:

Add the bases: 4 + 8 = 12
Multiply by height: 12 × 6 = 72
Multiply by $\frac{1}{2}$ : 72 ÷ 2 = 36

Remember to include square units in your final answer!

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