Calculate Trapezoid Area: 12 and 6 Unit Parallel Bases with 4 Unit Height

Trapezoid Area with Parallel Base Measurements

What is the area of the trapezoid in the figure?

121212666444AAABBBCCCDDDEEE

❤️ 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'll use the formula for calculating trapezoid area
00:07 (Sum of bases(AB+DC) multiplied by height(H))divided by 2
00:16 We'll substitute appropriate values according to the given data and solve for the area
00:23 In this case the height is AE
00:33 We'll divide 4 by 2
00:38 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

What is the area of the trapezoid in the figure?

121212666444AAABBBCCCDDDEEE

2

Step-by-step solution

The area of a trapezoid is calculated using the formula:

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

Given:

  • Base1=AB=12\text{Base}_{1} = AB = 12 units
  • Base2=CD=6\text{Base}_{2} = CD = 6 units
  • Height=h=4\text{Height} = h = 4 units

Plug these values into the formula:

Area=12×(12+6)×4 \text{Area} = \frac{1}{2} \times (12 + 6) \times 4

Calculate the sum of the bases:

12+6=18 12 + 6 = 18

Multiply by the height and divide by 2:

Area=12×18×4 \text{Area} = \frac{1}{2} \times 18 \times 4

Area=36 \text{Area} = 36 square units

Therefore, the area of the trapezoid is 36\mathbf{36} cm².

3

Final Answer

36 36 cm².

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area = ½ × (base₁ + base₂) × height
  • Technique: Add bases first: 12 + 6 = 18, then multiply by 4
  • Check: ½ × 18 × 4 = 36 square units ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to divide by 2 in the trapezoid formula
    Don't calculate (12 + 6) × 4 = 72 and call it done! This gives double the actual area because you forgot the ½ factor. Always remember the trapezoid formula includes dividing by 2: Area = ½ × (base₁ + base₂) × height.

Practice Quiz

Test your knowledge with interactive questions

Given the following trapezoid:

AAABBBCCCDDD584

Calculate the area of the trapezoid ABCD.

FAQ

Everything you need to know about this question

Why do we divide by 2 in the trapezoid formula?

+

The trapezoid formula comes from averaging the two parallel bases! Think of it as: (average of bases) × height. Since 12+62=9 \frac{12 + 6}{2} = 9 , then 9 × 4 = 36.

Which sides are the bases in this trapezoid?

+

The parallel sides are always the bases! In this figure, AB (length 12) and CD (length 6) are parallel to each other, so these are your two bases.

What if the trapezoid is tilted or rotated?

+

The formula works the same way! The height is always perpendicular to the parallel bases, no matter how the trapezoid is oriented on the page.

Can I use this formula for rectangles and parallelograms?

+

Yes! A rectangle is a special trapezoid where both bases are equal length. If base₁ = base₂ = 8, then Area = ½ × (8 + 8) × height = 8 × height.

What units should my answer have?

+

Since we're measuring area, always use square units like cm², m², or units². The problem shows lengths in units, so the area is 36 square units.

🌟 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