Calculate Trapezoid Area: Given Parallel Sides 5cm, 9cm and Height 7cm

Q: Which sides are the parallel bases in this trapezoid?

The parallel bases are AB = 5 cm and DC = 9 cm. These are the horizontal sides that run parallel to each other. The height is the perpendicular distance between these parallel sides.

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

The $ \frac{1}{2} $ factor finds the average of the two parallel bases! Think of it as: average base length × height. This gives the correct area since trapezoids are between triangles and rectangles.

Q: What if I mix up which measurements are the bases and height?

The height is always perpendicular to the parallel bases. In this problem, the dashed line shows h = 7 cm going straight down. The bases are the parallel sides: AB = 5 cm and DC = 9 cm.

Q: What units should my final answer have?

Always use square units for area! Since all measurements are in cm, your answer must be in cm². Don't forget to write cm² not just cm in your final answer.

Trapezoid Area with Parallel Base Measurements

The trapezoid ABCD is shown below.

AB = 5 cm

DC = 9 cm

Height (h) = 7 cm

Calculate the area of the trapezoid.

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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(AB+DC) multiplied by height (H)) divided by 2

00:14 Let's substitute appropriate values and solve to find the area

00:26 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.

AB = 5 cm

DC = 9 cm

Height (h) = 7 cm

Calculate the area of the trapezoid.

Step-by-step solution

The formula for the area of a trapezoid is:

\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}

We are given the following dimensions:

Base $AB = 5$ cm
Base $DC = 9$ cm
Height $h = 7$ cm

Substituting these values into the formula, we have:

\text{Area} = \frac{1}{2} \times (5 + 9) \times 7

First, add the lengths of the bases:

5 + 9 = 14

Now substitute back into the formula:

\text{Area} = \frac{1}{2} \times 14 \times 7

Calculate the multiplication:

\frac{1}{2} \times 14 = 7

Then multiply by the height:

7 \times 7 = 49

Thus, the area of the trapezoid is 49 cm $^2$ .

Final Answer

49 cm

Key Points to Remember

Essential concepts to master this topic

Formula: Area = $\frac{1}{2} \times (b_1 + b_2) \times h$ for trapezoids
Calculation: Add parallel bases first: 5 + 9 = 14 cm
Verification: Check units are squared (cm²) and result makes geometric sense ✓

Common Mistakes

Avoid these frequent errors

Using the wrong formula or forgetting the 1/2 factor
Don't use rectangle formula (base × height) = 98 cm²! This doubles the actual area because trapezoids aren't rectangles. Always multiply by 1/2 since the trapezoid formula averages the two parallel bases.

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

Which sides are the parallel bases in this trapezoid?

The parallel bases are AB = 5 cm and DC = 9 cm. These are the horizontal sides that run parallel to each other. The height is the perpendicular distance between these parallel sides.

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

The $\frac{1}{2}$ factor finds the average of the two parallel bases! Think of it as: average base length × height. This gives the correct area since trapezoids are between triangles and rectangles.

What if I mix up which measurements are the bases and height?

The height is always perpendicular to the parallel bases. In this problem, the dashed line shows h = 7 cm going straight down. The bases are the parallel sides: AB = 5 cm and DC = 9 cm.

Can I check my answer by drawing the trapezoid differently?

Yes! The area stays the same regardless of orientation. You could flip the trapezoid upside down or sideways - as long as you correctly identify the parallel bases and height, you'll get 49 cm².

What units should my final answer have?

Always use square units for area! Since all measurements are in cm, your answer must be in cm². Don't forget to write cm² not just cm in your final answer.

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Calculate Trapezoid Area: Given Parallel Sides 5cm, 9cm and Height 7cm

Trapezoid Area with Parallel Base Measurements

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Which sides are the parallel bases in this trapezoid?

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

What if I mix up which measurements are the bases and height?

Can I check my answer by drawing the trapezoid differently?

What units should my final answer have?

🌟 Unlock Your Math Potential

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