Calculate Trapezoid Height: Area 20 cm² with 10 cm Base Sum

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

The trapezoid formula $ S = \frac{(b_1 + b_2)}{2} \times h $ finds the average of the two parallel bases. Think of it as the width of a rectangle with the same area!

Q: What if I only know one base length instead of their sum?

You would need both individual base lengths or their sum to use this formula. If you only know one base, you'd need additional information like angles or side lengths.

Q: Can I solve this problem a different way?

This is the most direct method since you're given exactly what the formula needs: area and sum of bases. Other methods would require more complex calculations.

Q: How do I remember the trapezoid area formula?

Think: "Average base times height". The average of two numbers is their sum divided by 2, so $ \frac{(b_1 + b_2)}{2} $ gives you the average base length.

Trapezoid Area Formula with Given Base Sum

The trapezoid ABCD has an area equal to 20 cm².

The sum of its bases is 10 cm.

What is the height of the trapezoid?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the height of the trapezoid

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

00:06 (Sum of bases(AB+DC) multiplied by height(H)) divided by 2

00:14 We'll substitute appropriate values and solve for H

00:28 Let's isolate H

00:37 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The trapezoid ABCD has an area equal to 20 cm².

The sum of its bases is 10 cm.

What is the height of the trapezoid?

Step-by-step solution

To solve this problem, we'll use the trapezoid area formula:

Given:

Area, $S = 20 \, \text{cm}^2$
Sum of bases, $b_1 + b_2 = 10 \, \text{cm}$

The formula for the area of a trapezoid is:

S = \frac{(b_1 + b_2)}{2} \times h

Substituting the known values into the formula, we have:

20 = \frac{10}{2} \times h

Simplifying the equation:

20 = 5 \times h

Solving for $h$ , we divide both sides by 5:

h = \frac{20}{5} = 4 \, \text{cm}

Therefore, the height of the trapezoid is $4 \, \text{cm}$ .

Final Answer

4 cm

Key Points to Remember

Essential concepts to master this topic

Formula: Area = $\frac{(b_1 + b_2)}{2} \times h$ for trapezoid calculations
Technique: Substitute known values: $20 = \frac{10}{2} \times h$ then solve
Check: Verify by substituting back: $\frac{10}{2} \times 4 = 20$ cm² ✓

Common Mistakes

Avoid these frequent errors

Using wrong formula or forgetting to divide sum by 2
Don't use $S = (b_1 + b_2) \times h$ = 200 cm²! This gives an area 10 times too large because you forgot the division by 2. Always use the complete trapezoid formula with the fraction $\frac{(b_1 + b_2)}{2}$ .

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 the sum of bases by 2 in the trapezoid formula?

The trapezoid formula $S = \frac{(b_1 + b_2)}{2} \times h$ finds the average of the two parallel bases. Think of it as the width of a rectangle with the same area!

What if I only know one base length instead of their sum?

You would need both individual base lengths or their sum to use this formula. If you only know one base, you'd need additional information like angles or side lengths.

Can I solve this problem a different way?

This is the most direct method since you're given exactly what the formula needs: area and sum of bases. Other methods would require more complex calculations.

How do I remember the trapezoid area formula?

Think: "Average base times height". The average of two numbers is their sum divided by 2, so $\frac{(b_1 + b_2)}{2}$ gives you the average base length.

What units should my final answer have?

Since area is given in cm² and the sum is in cm, your height will be in cm (linear units). Always match the units given in the problem!

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