104 LearnersLast updated on August 30, 2025
Surface Area of Parallelogram
A parallelogram is a 2-dimensional shape with opposite sides parallel and equal in length. The surface area of a parallelogram is the total area covered by its surface, which is simply its area. In this article, we will learn about the surface area of a parallelogram.
What is the Surface Area of a Parallelogram?
The surface area of a parallelogram is the total area occupied by its surface.
It is measured in square units. A parallelogram is a 2D shape formed by two pairs of parallel sides.
The opposite sides are equal in length, and the opposite angles are equal.
Parallelograms include special types like rectangles, rhombuses, and squares.
Surface Area of a Parallelogram Formula
The surface area of a parallelogram is calculated using its base and height.
Look at the parallelogram below to see its base(b) and height(h).
The formula for the area of a parallelogram is: Area = base × height (b × h)
Base and Height of a Parallelogram
The base of a parallelogram is any one of its sides, and the height is the perpendicular distance from the base to the opposite side.
The formula for the area of a parallelogram is given as:
Area = b × h Here, b is the base of the parallelogram. h is the height of the parallelogram.
Properties of a Parallelogram
A parallelogram has several important properties:
1. Opposite sides are parallel and equal in length.
2. Opposite angles are equal.
3. Consecutive angles are supplementary (add up to 180 degrees).
4. The diagonals bisect each other.
These properties are useful in solving problems related to the area of a parallelogram.
Volume of a Parallelogram
Since a parallelogram is a 2-dimensional shape, it does not have volume. Volume is a concept applicable to 3-dimensional shapes. For a parallelogram, we focus on its area.
Confusion between Base and Height
Students sometimes mix up the base and height of a parallelogram. Always ensure the height is the perpendicular distance from the base to the opposite side, not the slanted side.
Mistake 1
Using Non-perpendicular Distance as Height
Some students mistakenly use the length of the slanted side instead of the perpendicular height. Remember, the height must be perpendicular to the base.
Mistake 2
Using Diagonal Lengths in Area Formula
A common mistake is using the lengths of the diagonals in the area formula. The diagonals are not used in calculating the area directly, only the base and height.
Mistake 3
Forgetting to Use the Correct Formula
Students sometimes forget the formula for the area of a parallelogram and confuse it with other shapes. Always use the formula: Area = base × height.
Mistake 4
Assuming All Parallelograms are Rectangles
Some students mistakenly believe all parallelograms are rectangles and use the properties of rectangles. Remember, while all rectangles are parallelograms, not all parallelograms are rectangles.
Mistake 5
Solved Examples of Surface Area of Parallelogram
Find the area of a parallelogram with a base of 8 cm and a height of 5 cm.
Area = 40 cm²
Problem 1
Given base = 8 cm, height = 5 cm. Use the formula: Area = base × height = 8 × 5 = 40 cm²
Find the area of a parallelogram with base 12 cm and height 7 cm.
Explanation
Area = 84 cm²
Problem 2
Use the formula: Area = base × height = 12 × 7 = 84 cm²
A parallelogram has a base of 10 cm and a height of 6 cm. Find the area.
Explanation
Area = 60 cm²
Problem 3
Use the formula: Area = base × height = 10 × 6 = 60 cm²
Find the area of a parallelogram with base 15 cm and height 3 cm.
Explanation
Area = 45 cm²
Problem 4
Area = base × height = 15 × 3 = 45 cm²
The height of a parallelogram is 8 cm, and its area is 64 cm². Find the base.
Explanation
Base = 8 cm
It is the total area that covers the surface of the parallelogram, calculated as base × height.
1.What are the properties of a parallelogram?
2.What is the difference between base and height?
3.Can a parallelogram have volume?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Parallelogram
Students often make mistakes while calculating the area of a parallelogram, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
