Calculate Trapezoid Area: Finding Area with Bases 5cm, 3cm and Height h

Trapezoid Area with Variable Height

Shown below is the trapezoid ABCD.

Given in cm:

AB = 5

DC = 3

Height = h

Calculate the area of the trapezoid.

555333hhhAAABBBCCCDDD

❤️ 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 area of the trapezoid
00:03 We will use the formula for calculating trapezoid area
00:07 (Sum of bases(AB+DC) multiplied by height (H)) divided by 2
00:14 We will substitute appropriate values and solve to find the area
00:23 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

Shown below is the trapezoid ABCD.

Given in cm:

AB = 5

DC = 3

Height = h

Calculate the area of the trapezoid.

555333hhhAAABBBCCCDDD

2

Step-by-step solution

Let's calculate the area of trapezoid ABCDABCD:

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}

In this trapezoid, we have:

  • Base1=AB=5\text{Base}_1 = AB = 5 cm
  • Base2=DC=3\text{Base}_2 = DC = 3 cm
  • Height=h\text{Height} = h

Substituting these into the formula, we get:

Area=12×(5+3)×h \text{Area} = \frac{1}{2} \times (5 + 3) \times h

Simplify the calculation:

Area=12×8×h=4h \text{Area} = \frac{1}{2} \times 8 \times h = 4h

Thus, the area of the trapezoid is 4h4h square centimeters.

3

Final Answer

4h 4h

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area = ½ × (sum of parallel bases) × height
  • Calculation: Substitute values: ½ × (5 + 3) × h = 4h
  • Check: Verify units match and expression simplifies correctly ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to divide by 2 in trapezoid formula
    Don't calculate (5 + 3) × h = 8h as final answer! This gives double the actual area because you missed the ½ factor. Always remember the trapezoid formula includes division by 2 to find the average base length.

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the trapezoid.

555141414666

FAQ

Everything you need to know about this question

Why do we add the two bases together first?

+

The trapezoid formula uses the average of the two parallel sides (bases). Adding 5 + 3 = 8, then multiplying by ½ gives us the average base length of 4.

What if the height was a number instead of h?

+

The process is exactly the same! If height was 6 cm, you'd calculate 12×(5+3)×6=24 \frac{1}{2} \times (5 + 3) \times 6 = 24 square cm.

How do I remember which sides are the bases?

+

The bases are the two parallel sides of the trapezoid. In this problem, AB and DC are parallel, so they're the bases (5 cm and 3 cm).

Can I use this formula for any trapezoid?

+

Yes! The formula Area=12×(b1+b2)×h \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h works for all trapezoids, as long as you identify the parallel sides correctly.

What units should my answer have?

+

Since we're finding area, the units are always square units. Here, with measurements in cm, the answer is 4h 4h square centimeters or cm².

🌟 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

More Questions

Click on any question to see the complete solution with step-by-step explanations

Area of a Trapezoid

Calculate Trapezoid Area: Finding Area of ABCD with Bases 5 and 8
Click to solve
Calculate Trapezoid Area: Finding the Space of ABCD with Height 5
Click to solve

Trapeze