Trapezoid Area Formula: Finding Height When Area = 20cm² and Base Sum = 10cm

Q: Why is there a ½ in the trapezoid area formula?

The ½ factor comes from averaging the two parallel bases! A trapezoid is like a triangle with its top cut off, so we use the average of both bases multiplied by height.

Q: What if I don't know the individual base lengths?

That's okay! The formula only needs the sum of the bases (b₁ + b₂). As long as you know this sum and the area, you can find the height without knowing each base separately.

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

The bases are always the two parallel sides of the trapezoid. In the diagram, these are the top side (AB) and bottom side (DC) that run horizontally.

Q: Can I use this method for any trapezoid?

Yes! This formula works for any trapezoid - whether it's right-angled, isosceles, or scalene. The key is identifying the two parallel sides as your bases.

Q: What if my calculation gives a decimal height?

Decimal heights are perfectly valid! Just make sure to round appropriately based on the precision of your given measurements and always check your work.

Trapezoid Area Formula with Given 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

00:04 We'll use the formula for calculating the area of a trapezoid

00:08 (Sum of bases(AB+DC) multiplied by height(H))divided by 2

00:13 We'll substitute appropriate values and solve for H

00:18 Let's isolate H

00:24 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

The formula for the area of a trapezoid is given by:

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

where $A$ is the area, $b_1$ and $b_2$ are the lengths of the two bases, and $h$ is the height.

We are given:

$A = 20 \, \text{cm}^2$
$b_1 + b_2 = 10 \, \text{cm}$

We substitute these values into the formula:

20 = \frac{1}{2} \times 10 \times h

To find $h$ , we simplify the equation:

20 = 5h

Dividing each side by 5, we get:

h = \frac{20}{5}

Hence, the height of the trapezoid is:

h = 4 \, \text{cm}

Therefore, the height of the trapezoid is 4 cm.

Final Answer

4 cm

Key Points to Remember

Essential concepts to master this topic

Formula: Area of trapezoid equals half times base sum times height
Technique: Substitute known values: $20 = \frac{1}{2} \times 10 \times h$
Check: Verify with formula: $\frac{1}{2} \times 10 \times 4 = 20 \text{ cm}^2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by 2 in the area formula
Don't use A = (b₁ + b₂) × h = 10 × h to get h = 2 cm! This ignores the ½ factor in the trapezoid formula and gives the wrong height. Always use the complete formula A = ½(b₁ + b₂)h with the fraction included.

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 is there a ½ in the trapezoid area formula?

The ½ factor comes from averaging the two parallel bases! A trapezoid is like a triangle with its top cut off, so we use the average of both bases multiplied by height.

What if I don't know the individual base lengths?

That's okay! The formula only needs the sum of the bases (b₁ + b₂). As long as you know this sum and the area, you can find the height without knowing each base separately.

How do I remember which sides are the bases?

The bases are always the two parallel sides of the trapezoid. In the diagram, these are the top side (AB) and bottom side (DC) that run horizontally.

Can I use this method for any trapezoid?

Yes! This formula works for any trapezoid - whether it's right-angled, isosceles, or scalene. The key is identifying the two parallel sides as your bases.

What if my calculation gives a decimal height?

Decimal heights are perfectly valid! Just make sure to round appropriately based on the precision of your given measurements and always check your work.

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