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

Q: Why do we divide by 2 in the trapezoid formula?

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

Q: Which side is the height in a trapezoid?

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.

Q: Can I get a decimal instead of a mixed number?

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

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

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

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

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

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.

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 $b_1 = 5$ .
Longer base $b_2 = 8$ .
Height $h = 3$ .

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

$A = \frac{1}{2} \times (b_1 + b_2) \times h$ .

Step 3: Substitute the given values into the formula:

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

Step 4: Perform the calculations:

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

$A = \frac{1}{2} \times 39$ .

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

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

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: $\frac{1}{2} \times (5 + 8) \times 3 = 19\frac{1}{2}$
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

Given the following trapezoid:

Calculate the area of the trapezoid ABCD.

FAQ

Everything you need to know about this question

Why do we divide by 2 in the trapezoid formula?

+

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

Which side is the height in a trapezoid?

+

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?

+

Yes! $19\frac{1}{2}$ 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?

+

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?

+

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

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

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