Area of Parallelogram: Formula, Examples, Practice Problems

A parallelogram can look tricky at first because its sides are slanted. But once students understand the difference between the base and the perpendicular height, finding its area becomes much easier.

The area of a parallelogram is: A = b × h

In this formula, b is the base, and h is the perpendicular height. To find the area, multiply the base by the height. Since area measures the space inside a shape, the answer should always be written in square units, such as square units, cm², in², or ft².

This guide will walk students through the parallelogram area formula step by step, with examples, real-life uses, practice problems, and common mistakes to avoid.

Quick Navigation

• What Is the Formula for the Area of a Parallelogram?
• How Do You Find the Area of a Parallelogram Step by Step?
• Try It First: Area of a Parallelogram Practice
• How Do You Solve Area of a Parallelogram Problems?
  • Example 1: How to Find the Area of a Parallelogram Using the Formula
  • Example 2: How to Find the Missing Base of a Parallelogram
  • Example 3: How to Find the Missing Height of a Parallelogram
  • Example 4: How to Use Parallelogram Area in Real Life
  • Example 5: How to Solve Composite Figures with Parallelograms
• Why Does the Parallelogram Area Formula Work?

What Is the Formula for the Area of a Parallelogram?

The formula is A = b × h, where b is the base and h is the perpendicular height. To find the area, multiply the base by the height.

Important: The height is the perpendicular distance, not the slanted side.

How to Find the Area of a Parallelogram Step by Step?

To find the area of a parallelogram, follow these steps:

1. Identify the base.
   Choose the side labeled as the base.
2. Find the perpendicular height.
   Look for the distance that forms a 90-degree angle with the base.
3. Multiply the base by the height.
   Use the formula: A = b × h.
4. Write the answer in square units.
   Area answers should use square units, such as cm², in², ft², or square units.

This step-by-step method helps students avoid confusing side length with height.

Try It First: Area of a Parallelogram Practice

You’ve learned the formula. Now try a few quick questions before reading the examples. This will help you check whether you can find the area, use the correct height, and avoid common mistakes.

Great job trying the practice! Next, let’s walk through different types of parallelogram area problems step by step.

How to Solve Area of a Parallelogram Problems?

The parallelogram area formula can be used in many types of problems. Students may need to find the area, find a missing base, find a missing height, solve a word problem, or work with a composite figure.

Below are six common example types.

Example 1: How to Find the Area of a Parallelogram?

Question: A parallelogram has a base of 12 units and a height of 8 units. What is the area?

Example 2: How to Find the Missing Base of a Parallelogram?

Question:
A parallelogram has an area of 72 square units and a height of 9 units. What is the base?

Step 1: Write the formula. A = b × h

Step 2: Substitute the known values. 72 = b × 9

Step 3: Divide both sides by 9. b = 72 ÷ 9, b = 8

Answer:
The base is 8 units.

Example 3: How to Find the Missing Height of a Parallelogram?

Question:
A parallelogram has an area of 96 square centimeters and a base of 12 centimeters. What is the height?

Step 1: Write the formula. A = b × h

Step 2: Substitute the known values. 96 = 12 × h

Step 3: Divide both sides by 12. h = 96 ÷ 12, h = 8

Answer:
The height is 8 centimeters.

You can also use the rearranged formula:

h = A ÷ b or b = A ÷ h

Example 4: How to Use Parallelogram Area in Real Life?

Parallelogram area appears in real-life situations involving design, construction, flooring, fabric, tiling, and patterns.

Question:
A floor tile is shaped like a parallelogram. The base is 10 inches, and the perpendicular height is 6 inches. What area does one tile cover?

A = b × h = 10 × 6 = 60

Answer:
One tile covers 60 square inches.

Why this matters:
This type of problem helps students connect geometry to real-life measurement. Area is used when planning floors, walls, gardens, fabric patterns, and design projects.

Example 5: How to Solve Composite Figures with Parallelograms

Sometimes a figure is made of more than one shape. These are called composite figures. To find the total area, students can break the figure into smaller shapes, find each area, and add them together.

Question:
A design is made of a rectangle and a parallelogram. The rectangle is 8 cm long and 5 cm wide. The parallelogram has a base of 8 cm and a height of 4 cm. What is the total area?

Why Does the Parallelogram Area Formula Work?

Let's break it down!

Here is a parallelogram. If you cut off a triangle from one side and slide it to the other, you can form a rectangle! This neat transformation doesn't change the area.

That's why the area of a parallelogram uses the same idea as the area of a rectangle:

Area the Parallelogram = base × height

Important tip: The height is not the side of the parallelogram—unless that side forms a right angle with the base! Think of height as the straight-up distance from the base to the top, like a ladder standing tall and perfectly upright.

What Is the Difference Between Base, Height, and Side Length?

To use the area formula correctly, it is important to understand the difference between the base, height, and side length.

What is a parallelogram?

A parallelogram is defined as a quadrilateral (a four-sided polygon) where both pairs of opposite sides are parallel. When finding the area of a parallelogram, the two most important parts are the base and the height.

What is the base?

The base is the side you choose to measure from.

• If the parallelogram is sitting flat, the bottom edge is usually the base.

• If it's tilted or slanted, any side can be used as the base — as long as we know how to find the correct height for it!

What is the height?

The height is the straight-up distance from the base to the opposite side.

• The height must be perpendicular to the base.
• That means it forms a 90° angle with the base.

Sometimes, the height falls outside the parallelogram. That's totally okay! Just imagine dropping a straight line from the top down to the base. As long as it's at a right angle, it counts as the height.

So whether the base is flat or slanted, the rule is the same: Height must be perpendicular to the base, even if it's outside the shape!

Once you know the base and the correct height, you can use the formula A = b × h with confidence.

What is the side length?

The side length is different from the height.

• A slanted side may look like the height.
• But it is not the height unless it forms a right angle with the base.

Measurement	What It Means	Can You Use It in A = b × h?
Base	The chosen side of the parallelogram	Yes
Height	Perpendicular distance to the opposite side	Yes
Slanted side	A side length that leans	Usually no

Key Reminder:
The base and height must match. If you choose a different base, you may need a different perpendicular height.

5 Common Mistakes When Finding the Area of a Parallelogram

Even when you know the formula A = b × h, you may still make small mistakes that lead to the wrong answer. Here are some of the most common ones and how to fix them.

1. Using the slanted side instead of the height

One of the most common mistakes is using the slanted side as the height. In a parallelogram, the slanted side may look like the height, but it is only the height if it forms a right angle with the base.

• How to avoid this mistake: Always check whether the line is perpendicular to the base. If it is not, it is a side length, not the height.

2. Pairing the Wrong Base with the Wrong Height

A parallelogram can have more than one possible base, but each base has its own matching height.

• How to avoid this mistake: Use the height that is perpendicular to the base you choose.

If the base is horizontal, the height should be the vertical distance between the two horizontal sides. If you choose a slanted side as the base, the height must be perpendicular to that slanted side.

3. Forgetting square units in the final answer

Area measures the amount of space inside a shape, so the answer should always be written in square units, such as square inches, square centimeters, or square feet.

• How to avoid this mistake: After solving, check your final answer and make sure the unit is written as units², such as cm² or in².

4. Confusing Perimeter and Area

Perimeter measures the distance around a shape. Area measures the space inside a shape.

For a parallelogram:

• Area uses base × height.
• Perimeter uses the lengths of all four sides.

How to avoid this mistake: Ask “Am I measuring around the shape or inside the shape?”

5. Forgetting to Convert Units

Sometimes the base and height are given in different units.

For example:

• base = 2 feet
• height = 12 inches

Before multiplying, students should convert the units so both measurements use the same unit.

How to avoid this mistake: Check the units before using the formula.

More Practice: Area of a Parallelogram Practice Problems

Try these practice problems to check your understanding.

Practice Problem 1

A parallelogram has a base of 6 units and a height of 5 units. What is the area?

Practice Problem 2

A parallelogram has a base of 14 inches and a height of 9 inches. What is the area?

Practice Problem 3

A parallelogram has an area of 80 square units and a height of 10 units. What is the base?

Practice Problem 4

A parallelogram has an area of 63 square centimeters and a base of 9 centimeters. What is the height?

Practice Problem 5

A parallelogram has a base of 8.5 feet and a height of 4 feet. What is the area?

Practice Problem 6

A parallelogram has a base of 12 meters and a height of 3/4 meter. What is the area?

Practice Problem 7

A fabric pattern is shaped like a parallelogram. Its base is 15 inches and its height is 8 inches. How much fabric does the pattern cover?

Practice Problem 8

A composite figure is made of a rectangle and a parallelogram. The rectangle is 10 cm long and 4 cm wide. The parallelogram has a base of 10 cm and a height of 3 cm. What is the total area?

Answer Key

Problem	Answer
1	30 square units
2	126 square inches
3	8 units
4	7 centimeters
5	34 square feet
6	9 square meters
7	120 square inches
8	70 square centimeters

What Other Area Formulas Should Students Know?

Understanding parallelogram area is part of a larger geometry learning path. Students should also know how to find the area of squares, rectangles, triangles, trapezoids, and circles.

To help you see how parallelograms fit into the big picture of geometry, here's a quick summary of the area formulas for some common shapes:

Shape	Figure	Area Formula	Special Notes
Square		Area = side²	All four sides are equal
Rectangle		Area = length × width	Opposite sides are equal
Triangle		Area = ½ × base × height	Three sides
Parallelogram		Area = base × height	Opposite sides are parallel
Trapezoid		Area = ½ × (base₁ + base₂) × height	One pair of parallel sides
Circle		Area = π × radius²	The radius is the distance from the center to the edge of the circle

Additional Math Topics in Geometry for Grade 6-7

• Grade 6 Math Guide
• Pre-Algebra Math Guide
• Angles
• Area of Triangles
• Area of Trapezoids
• Parallel lines
• Perpendicular lines
• Pythagorean theorem
• Congruent triangles
• Similar triangles
• Circles
• Coordinate Plane

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