Find Diagonal AC: Square and Parallelogram with Area 100

Q: Why is ED the height and not side AF?

The height of a parallelogram must be perpendicular to the base. ED is drawn vertically down from the base AC, making it the true height. Side AF is slanted, so it's longer than the actual height.

Q: How do I know which side is the base?

You can choose any side as the base! In this problem, we're finding AC, so we treat AC as the base and use the perpendicular height ED = 5.

Q: What's the difference between a square and parallelogram area?

Both use $ \text{Area} = \text{base} \times \text{height} $. For squares, base = height, but parallelograms have different base and height measurements.

Q: Can I use the Pythagorean theorem here?

No need! We already have the height (ED = 5) and area (100). Just use the area formula: $ \text{Area} = \text{base} \times \text{height} $.

Q: How do I solve for AC from the area formula?

Set up the equation: $ 100 = AC \times 5 $. Then divide both sides by 5: $ AC = \frac{100}{5} = 20 $.

Parallelogram Area with Height Formula

The square ABCD and the parallelogram AFED are shown below.

The area of the parallelogram is equal to 100.

ED = 5

How long is AC?

❤️ 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 Find AC

00:03 Side length according to the given data

00:07 We'll use the formula for calculating parallelogram area (side times side)

00:13 Multiply by AC as it is the external height to the side

00:20 We'll substitute appropriate values according to the given data and solve for AC

00:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The square ABCD and the parallelogram AFED are shown below.

The area of the parallelogram is equal to 100.

ED = 5

How long is AC?

Step-by-step solution

The area of a parallelogram is equal to the side multiplied by the height, as we know that ED is equal to 5, the area is also given.

We place the data in the following formula:

$S=AC\times ED$

$100=AC\times5$

We divide by 5 the two sections:

$\frac{100}{5}=\frac{5AC}{5}$

$20=AC$

Final Answer

$20$

Key Points to Remember

Essential concepts to master this topic

Area Formula: Parallelogram area equals base times perpendicular height
Technique: Use Area = base × height, so 100 = AC × 5
Check: Verify AC = 20 by calculating 20 × 5 = 100 ✓

Common Mistakes

Avoid these frequent errors

Using side length instead of perpendicular height
Don't use slanted side FE as height = wrong area calculation! The slanted side isn't perpendicular to the base, so it doesn't represent the true height. Always use the perpendicular distance (ED = 5) as the height.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

Is a parallelogram a square?

FAQ

Everything you need to know about this question

Why is ED the height and not side AF?

The height of a parallelogram must be perpendicular to the base. ED is drawn vertically down from the base AC, making it the true height. Side AF is slanted, so it's longer than the actual height.

How do I know which side is the base?

You can choose any side as the base! In this problem, we're finding AC, so we treat AC as the base and use the perpendicular height ED = 5.

What's the difference between a square and parallelogram area?

Both use $\text{Area} = \text{base} \times \text{height}$ . For squares, base = height, but parallelograms have different base and height measurements.

Can I use the Pythagorean theorem here?

No need! We already have the height (ED = 5) and area (100). Just use the area formula: $\text{Area} = \text{base} \times \text{height}$ .

How do I solve for AC from the area formula?

Set up the equation: $100 = AC \times 5$ . Then divide both sides by 5: $AC = \frac{100}{5} = 20$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Square for 9th Grade 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