Calculate Isosceles Trapezoid Area: Given h=5cm, P=34cm, and BC=7cm

Trapezoid Area with Perimeter Constraints

Shown below is the isosceles trapezoid ABCD.

Given in cm:
BC = 7

Height of the trapezoid (h) = 5

Perimeter of the trapezoid (P) = 34

Calculate the area of the trapezoid.

777h=5h=5h=5AAABBBCCCDDDEEE

❤️ 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 the area of a trapezoid
00:07 (Sum of bases(AB+DC) multiplied by height (H)) divided by 2
00:12 The perimeter of the trapezoid equals the sum of its sides
00:22 According to the given data, it's an isosceles trapezoid
00:27 Let's substitute appropriate values to find the sum of the bases
00:41 Let's isolate the sum of bases(AB+DC)
00:45 This is the size of the sum of bases
00:49 Now let's substitute appropriate values in the area formula and calculate the area
00:57 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 isosceles trapezoid ABCD.

Given in cm:
BC = 7

Height of the trapezoid (h) = 5

Perimeter of the trapezoid (P) = 34

Calculate the area of the trapezoid.

777h=5h=5h=5AAABBBCCCDDDEEE

2

Step-by-step solution

Since ABCD is a trapezoid, one can determine that:

AD=BC=7 AD=BC=7

Thus the formula to find the area will be

SABCD=(AB+DC)×h2 S_{ABCD}=\frac{(AB+DC)\times h}{2}

Since we are given the perimeter of the trapezoid, we can findAB+DC AB+DC

PABCD=7+AB+7+DC P_{ABCD}=7+AB+7+DC

34=14+AB+DC 34=14+AB+DC

3414=AB+DC 34-14=AB+DC

20=AB+DC 20=AB+DC

Now we will place the data we obtained into the formula in order to calculate the area of the trapezoid:

S=20×52=1002=50 S=\frac{20\times5}{2}=\frac{100}{2}=50

3

Final Answer

50

Key Points to Remember

Essential concepts to master this topic
  • Property: Isosceles trapezoid has equal non-parallel sides
  • Technique: Use perimeter P = AD + AB + BC + DC to find parallel sides sum
  • Check: Area = (AB+DC)×h2=20×52=50 \frac{(AB+DC)\times h}{2} = \frac{20\times 5}{2} = 50

Common Mistakes

Avoid these frequent errors
  • Using given side BC as both equal sides
    Don't assume BC = 7 means AB = 7 too = wrong parallel sides! In an isosceles trapezoid, the equal sides are the non-parallel ones (AD and BC). Always identify that AD = BC = 7, then use perimeter to find AB + DC.

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the trapezoid.

555141414666

FAQ

Everything you need to know about this question

What makes a trapezoid 'isosceles'?

+

An isosceles trapezoid has equal non-parallel sides! In trapezoid ABCD, the parallel sides are AB and DC, so the equal sides are AD = BC = 7.

Why can't I use the regular trapezoid formula directly?

+

You can! But first you need to find the lengths of both parallel sides. Use the perimeter constraint to find AB + DC, then apply Area=(AB+DC)×h2 Area = \frac{(AB+DC)\times h}{2} .

How do I find the parallel sides from the perimeter?

+

Since P = AD + AB + BC + DC and AD = BC = 7:

  • 34 = 7 + AB + 7 + DC
  • 34 = 14 + AB + DC
  • AB + DC = 20

What if I calculated AB + DC = 34 - 7 = 27?

+

That's a common error! Remember there are two equal sides: AD = BC = 7. So you subtract both: 34 - 7 - 7 = 20, not just one side.

Can I solve this without finding individual side lengths?

+

Yes! You only need the sum of parallel sides (AB + DC = 20) for the area formula. No need to find AB and DC separately!

🌟 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