Calculate Parallelogram Perimeter: Given Area 39 cm² and Height 3 cm

Q: How do I know which side goes with the height of 3 cm?

The height is always perpendicular to the base. Look at the diagram - the height line drops straight down from the top, making it perpendicular to side AB, not AC.

Q: Why can't I use AC = 8 cm with the height?

The height of 3 cm is not perpendicular to AC. In parallelograms, each side can have its own corresponding height, and you must match them correctly for the area formula.

Q: How do I remember the parallelogram perimeter formula?

Think "opposite sides are equal"! So perimeter = 2 × (first side) + 2 × (adjacent side). Just like a rectangle, but the sides might not be perpendicular.

Q: Can I solve this without finding AB first?

No! You need both side lengths to calculate perimeter. Since you only know AC = 8 cm, you must use the area formula to find AB before calculating the perimeter.

Parallelogram Perimeter with Area Applications

Given the parallelogram whose area is equal to 39 cm² and AC=8 cm and the height of the rectangle is 3 cm:

Calculate the perimeter 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 perimeter of the parallelogram

00:03 We'll use the formula to calculate the area of a parallelogram

00:07 Side (CD) multiplied by height (H)

00:11 We'll substitute appropriate values and solve to find CD 00:1

00:16 Let's isolate CD

00:28 And this is the length of side CD

00:33 Opposite sides are equal in a parallelogram

00:50 The perimeter of the parallelogram equals the sum of its sides

01:01 We'll substitute appropriate values and solve for the perimeter

01:10 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

Given the parallelogram whose area is equal to 39 cm² and AC=8 cm and the height of the rectangle is 3 cm:

Calculate the perimeter of the parallelogram.

Step-by-step solution

The area of a parallelogram is equal to the side multiplied by the height of that side.

First, find the value of AB using the parallelogram area formula:

$AB\times h=S$

$AB\times3=39$

$\frac{3AB}{3}=\frac{39}{3}$

$AB=13$

Since in a parallelogram all pairs of opposite sides are equal and parallel, we can find the perimeter of the parallelogram:

$2AB+2AC=2\times13+2\times8=26+16=42$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Parallelogram area equals base times corresponding height
Technique: Use $AB \times 3 = 39$ to find AB = 13 cm
Check: Verify perimeter: 2(13) + 2(8) = 42 cm ✓

Common Mistakes

Avoid these frequent errors

Using AC as the base for the given height
Don't assume AC = 8 cm goes with height 3 cm = wrong base-height pair! The height is perpendicular to AB, not AC, so you can't use AC in the area formula. Always identify which side the height corresponds to before calculating.

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

How do I know which side goes with the height of 3 cm?

The height is always perpendicular to the base. Look at the diagram - the height line drops straight down from the top, making it perpendicular to side AB, not AC.

Why can't I use AC = 8 cm with the height?

The height of 3 cm is not perpendicular to AC. In parallelograms, each side can have its own corresponding height, and you must match them correctly for the area formula.

What if I calculated AB = 8 and AC = 13?

That would give you perimeter = 42 cm too, but it's wrong! The problem clearly states AC = 8 cm, so you must use the area formula to find AB = 13 cm.

How do I remember the parallelogram perimeter formula?

Think "opposite sides are equal"! So perimeter = 2 × (first side) + 2 × (adjacent side). Just like a rectangle, but the sides might not be perpendicular.

Can I solve this without finding AB first?

No! You need both side lengths to calculate perimeter. Since you only know AC = 8 cm, you must use the area formula to find AB before calculating the perimeter.

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