Calculate Parallelogram Area: Given Perimeter 60 and Height 3

Q: Why do I use 4x as the base instead of 2x?

Look at the diagram carefully! The height line is perpendicular to the side labeled 4x, making it the correct base. The 2x side is slanted, so you can't use it with this height.

Q: How do I know which sides are equal in a parallelogram?

Opposite sides are always equal in a parallelogram. So if one side is 4x, the side directly across from it is also 4x. Same for the 2x sides.

Q: What if I calculated the perimeter wrong?

Double-check by adding all four sides: 4x + 2x + 4x + 2x = 12x. Set this equal to the given perimeter (60) to solve for x.

Q: Can I use the 2x side and find a different height?

Theoretically yes, but the problem gives you the height that goes with the 4x base. Using a different base would require a different height measurement that isn't provided.

Q: Why is the area formula base × height and not length × width?

For parallelograms, we use base × height because the height is the perpendicular distance between parallel sides. This gives the true area, unlike multiplying two slanted sides.

Parallelogram Area with Perimeter Constraints

Below is a parallelogram with a perimeter of 60 and a height of 3.

Calculate the area of the parallelogram.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the area of the parallelogram

00:04 Opposite sides are equal in a parallelogram

00:16 Let's substitute the side values

00:29 The perimeter of the parallelogram equals the sum of its sides

00:42 Let's substitute appropriate values and solve for X

01:07 This is the value of X

01:11 Now let's use the formula for calculating the area of a parallelogram

01:15 Side (CD) multiplied by the height to side (H)

01:22 Let's substitute appropriate values and solve for the area

01:38 Let's substitute the X value we found earlier

01:47 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Below is a parallelogram with a perimeter of 60 and a height of 3.

Calculate the area of the parallelogram.

Step-by-step solution

As is true for a parallelogram each pair of opposite sides are equal to one other:

$AB=CD=4x,AC=BD=2x$

To begin we will find X through the perimeter: $60=2x+4x+2x+4x$

$60=12x$

$x=5$

Next we will calculate all of the sides of the parallelogram:

$AB=CD=4\times5=20$

$AC=BD=2\times5=10$

Hence the area of the parallelogram will be equal to:

$CD\times3=20\times3=60$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = base × height for any parallelogram
Method: Use perimeter to find sides: 60 = 12x, so x = 5
Check: Base = 20, height = 3, so area = 20 × 3 = 60 ✓

Common Mistakes

Avoid these frequent errors

Using the wrong side as the base
Don't multiply the slanted side by height = wrong area! The height is always perpendicular to the base, not the slanted side. Always use the side that's perpendicular to the given height measurement.

Practice Quiz

Test your knowledge with interactive questions

Find the perimeter of the parallelogram using the data below.

FAQ

Everything you need to know about this question

Why do I use 4x as the base instead of 2x?

Look at the diagram carefully! The height line is perpendicular to the side labeled 4x, making it the correct base. The 2x side is slanted, so you can't use it with this height.

How do I know which sides are equal in a parallelogram?

Opposite sides are always equal in a parallelogram. So if one side is 4x, the side directly across from it is also 4x. Same for the 2x sides.

What if I calculated the perimeter wrong?

Double-check by adding all four sides: 4x + 2x + 4x + 2x = 12x. Set this equal to the given perimeter (60) to solve for x.

Can I use the 2x side and find a different height?

Theoretically yes, but the problem gives you the height that goes with the 4x base. Using a different base would require a different height measurement that isn't provided.

Why is the area formula base × height and not length × width?

For parallelograms, we use base × height because the height is the perpendicular distance between parallel sides. This gives the true area, unlike multiplying two slanted sides.

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