Calculate Trapezoid Area: Finding Space Between 7 and 15 Unit Parallel Sides

Trapezoid Area with Parallel Base Measurements

What is the area of the trapezoid in the figure?

777151515222AAABBBCCCDDDEEE

❤️ 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 Let's use the formula for calculating trapezoid area
00:08 (Sum of bases(AB+DC) multiplied by height(H)) divided by 2
00:14 Let's substitute appropriate values according to the given data and solve for the area
00:21 In this case, the height is BE
00:25 Let's reduce by 2
00:30 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?

777151515222AAABBBCCCDDDEEE

2

Step-by-step solution

We use the following formula to calculate the area of a trapezoid: (base+base) multiplied by the height divided by 2:

(AB+DC)×BE2 \frac{(AB+DC)\times BE}{2}

(7+15)×22=22×22=442=22 \frac{(7+15)\times2}{2}=\frac{22\times2}{2}=\frac{44}{2}=22

3

Final Answer

22 22 cm².

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area equals sum of parallel bases times height divided by 2
  • Technique: Add bases first: (7 + 15) = 22, then multiply by height 2
  • Check: Units should be square units, and result should be reasonable for given dimensions ✓

Common Mistakes

Avoid these frequent errors
  • Using the wrong formula or confusing base with height
    Don't use rectangle formula (length × width) or triangle formula = completely wrong answer! Trapezoids have two different parallel bases that must be added together. Always use the trapezoid formula: (base₁ + base₂) × height ÷ 2.

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

How do I identify which sides are the bases and which is the height?

+

The bases are the two parallel sides (here 7 and 15 units). The height is the perpendicular distance between them (here 2 units). Look for the right angle symbol to identify the height!

Why do we divide by 2 in the trapezoid formula?

+

Think of it as finding the average of the two bases, then multiplying by height. 7+152=11 \frac{7+15}{2} = 11 (average base) × 2 (height) = 22. This gives the same result as our formula!

What if the trapezoid looks upside down?

+

It doesn't matter which way the trapezoid is oriented! The formula works the same way. Just identify the two parallel sides as your bases and the perpendicular distance as height.

Can I use this formula for rectangles and parallelograms too?

+

Yes! A rectangle is just a special trapezoid where both bases are equal. If bases are 5 and 5, then (5+5)×h2=10h2=5h \frac{(5+5) \times h}{2} = \frac{10h}{2} = 5h , which is length × width!

How do I know if my answer makes sense?

+

Check if your area is between what you'd get for triangles and rectangles with the same dimensions. Here: triangle area would be 15×22=15 \frac{15 \times 2}{2} = 15 , rectangle would be 15×2=30 15 \times 2 = 30 . Our answer 22 fits perfectly between them!

🌟 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