Trapezoid Length Calculation: Finding BC When Area is 100 cm²

Q: Why do we add both bases together in the formula?

A trapezoid has two parallel bases of different lengths. The formula $ \frac{1}{2} \times (b_1 + b_2) \times h $ finds the average of the two bases, then multiplies by height - like finding the area of a rectangle with the average width!

Q: How do I know which sides are the bases?

The bases are the parallel sides of the trapezoid. In this problem, AD and BC are parallel and horizontal, so they're the bases. The height is always perpendicular to these parallel sides.

Q: Can I use this same method for any trapezoid problem?

Yes! This substitution method works for any trapezoid area problem. Just identify what you know (area, height, one base) and solve for the unknown base using algebra.

Q: Why is the height drawn from C to the bottom?

The height must be perpendicular to the parallel bases. Point E shows where the perpendicular from C meets the bottom base AD, creating the 8 cm height measurement.

Trapezoid Area Formula with Base Calculation

The area of trapezoid

ABCD is 100 cm².

The height of trapezoid CE is 8 cm.

The base of trapezoid AD is 15 cm.

Calculate the length of BC.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the length of base BC

00:03 We'll use the formula for calculating trapezoid area

00:12 ((sum of bases) times height) divided by 2

00:24 We'll substitute appropriate values according to the given data and solve for BC

00:59 We'll isolate BC

01:24 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 area of trapezoid

ABCD is 100 cm².

The height of trapezoid CE is 8 cm.

The base of trapezoid AD is 15 cm.

Calculate the length of BC.

Step-by-step solution

We'll begin by using the formula for the area of a trapezoid:

$A = \frac{1}{2} \times (a + b) \times h$

where:

$A$ is the area of the trapezoid, which is 100 cm².
$a$ is the length of base AD, which is 15 cm.
$b$ is the length of base BC, which we need to find.
$h$ is the height of the trapezoid, which is 8 cm.

Substituting the known values into the formula, we have:

$100 = \frac{1}{2} \times (15 + b) \times 8$

First, simplify the right side of the equation:

$100 = 4 \times (15 + b)$

Next, divide both sides by 4 to isolate the terms inside the parenthesis:

$25 = 15 + b$

Finally, subtract 15 from both sides to solve for $b$ :

$b = 25 - 15 = 10$

Therefore, the length of base BC is $\mathbf{10}$ cm.

The solution to the problem is $\boxed{10}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = (1/2) × (base₁ + base₂) × height
Technique: Substitute known values: 100 = (1/2) × (15 + b) × 8
Check: Verify: (1/2) × (15 + 10) × 8 = 100 ✓

Common Mistakes

Avoid these frequent errors

Using only one base in the area formula
Don't use Area = base × height like a rectangle = wrong formula! A trapezoid has two different parallel bases that must both be included. Always use Area = (1/2) × (base₁ + base₂) × height 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 we add both bases together in the formula?

A trapezoid has two parallel bases of different lengths. The formula $\frac{1}{2} \times (b_1 + b_2) \times h$ finds the average of the two bases, then multiplies by height - like finding the area of a rectangle with the average width!

How do I know which sides are the bases?

The bases are the parallel sides of the trapezoid. In this problem, AD and BC are parallel and horizontal, so they're the bases. The height is always perpendicular to these parallel sides.

What if I get a negative answer for the base length?

A negative length doesn't make sense! Check your arithmetic - you might have subtracted incorrectly. Base lengths must always be positive numbers.

Can I use this same method for any trapezoid problem?

Yes! This substitution method works for any trapezoid area problem. Just identify what you know (area, height, one base) and solve for the unknown base using algebra.

Why is the height drawn from C to the bottom?

The height must be perpendicular to the parallel bases. Point E shows where the perpendicular from C meets the bottom base AD, creating the 8 cm height measurement.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Trapeze questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime