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

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.

555999h=7h=7h=7AAABBBCCCDDD

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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
1

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.

555999h=7h=7h=7AAABBBCCCDDD

2

Step-by-step solution

The formula for the area of a trapezoid is:

Area=12×(Base1+Base2)×Height \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}

We are given the following dimensions:

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

Substituting these values into the formula, we have:

Area=12×(5+9)×7 \text{Area} = \frac{1}{2} \times (5 + 9) \times 7

First, add the lengths of the bases:

5+9=14 5 + 9 = 14

Now substitute back into the formula:

Area=12×14×7 \text{Area} = \frac{1}{2} \times 14 \times 7

Calculate the multiplication:

12×14=7 \frac{1}{2} \times 14 = 7

Then multiply by the height:

7×7=49 7 \times 7 = 49

Thus, the area of the trapezoid is 49 cm2^2.

3

Final Answer

49 cm

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area = 12×(b1+b2)×h \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

Calculate the area of the trapezoid.

555141414666

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 12 \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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