Calculate Parallelogram Height AE Using Area = 40 cm² and Base = 8 units

Area Formula with Height Calculation

Look at the parallelogram in the figure below.

Its area is equal to 40 cm².

Calculate AE.

888AAABBBCCCDDDEEE

❤️ 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
00:06 First, we need to find AE, the height.
00:10 Remember, in a parallelogram, opposite sides are equal.
00:27 Now, let's use the area formula for a parallelogram.
00:31 The formula is side length CD times height AE.
00:39 We'll substitute the values we have and solve for AE.
00:55 And that's how we solve for AE. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the parallelogram in the figure below.

Its area is equal to 40 cm².

Calculate AE.

888AAABBBCCCDDDEEE

2

Step-by-step solution

We are told that ABCD is a parallelogram,AB=CD=8 AB=CD=8 According to the properties of a parallelogram, each pair of opposite sides are equal and parallel.

Hence to find AE we will need to use the area given to us in the formula in order to determine the area of the parallelogram:

S=DC×AE S=DC\times AE

40=8×AE 40=8\times AE

We divide both sides of the equation by 8:

8AE:8=40:8 8AE:8=40:8

AE=5 AE=5

3

Final Answer

5 5 cm

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of parallelogram equals base times height
  • Technique: Rearrange A=b×h A = b \times h to get h=Ab h = \frac{A}{b}
  • Check: Verify 8×5=40 8 \times 5 = 40 cm² matches given area ✓

Common Mistakes

Avoid these frequent errors
  • Confusing side length with height
    Don't use the slanted side BC as the height = wrong calculation! The height must be perpendicular to the base, not parallel. Always use the perpendicular distance AE when the base is horizontal.

Practice Quiz

Test your knowledge with interactive questions

A parallelogram has a length equal to 6 cm and a height equal to 4.5 cm.

Calculate the area of the parallelogram.

6664.54.54.5

FAQ

Everything you need to know about this question

Why can't I use side BC as the height?

+

The height must be perpendicular to the base! Side BC is slanted (parallel to AD), but height AE drops straight down at a 90° angle to the base AB.

How do I know which measurement is the base?

+

The problem shows AB = 8 units as the horizontal side, making it our base. The height AE is the perpendicular distance from this base to the opposite side.

What if I get a decimal answer?

+

That's perfectly normal! Many geometry problems have decimal heights. Just make sure your calculation is correct: 408=5 \frac{40}{8} = 5 .

Can I use a different side as the base?

+

Yes! You could use any side as the base, but then you'd need the perpendicular height to that side. The area formula A=b×h A = b \times h always works.

How do I remember the area formula?

+

Think of it like a rectangle! A parallelogram's area is base × height, just like length × width for rectangles. The key is using the perpendicular height, not the slanted side.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parallelogram 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