101 LearnersLast updated on August 30, 2025
Surface Area of Quadrilateral
A quadrilateral is a 2-dimensional shape with four sides. The surface area of a quadrilateral is the total area covered by its outer surface. In this article, we will learn about the surface area of different types of quadrilaterals, including squares, rectangles, and trapezoids.
What is the Surface Area of a Quadrilateral?
The surface area of a quadrilateral is the total area occupied by its outer boundary.
It is measured in square units.
A quadrilateral is a 2D shape with four sides and four angles.
The most common types of quadrilaterals are squares, rectangles, parallelograms, rhombuses, trapezoids, and kites.
Each type has its own formula for calculating the surface area based on its specific properties.
Surface Area of a Quadrilateral Formula
The formula for the surface area of a quadrilateral varies based on the type of quadrilateral. Here are the formulas for some common quadrilaterals:
Square: Area = side² - Rectangle: Area = length × width
Parallelogram: Area = base × height
Trapezoid: Area = ½ × (base₁ + base₂) × height
Surface Area of a Square
The area of a square is calculated by squaring the length of its side.
The formula for the area of a square is: Area = side²
Here, 'side' is the length of any of the square's four sides.
Surface Area of a Rectangle
The area of a rectangle is calculated by multiplying its length by its width.
The formula is: Area = length × width Where 'length' is the longer side, and 'width' is the shorter side of the rectangle.
Surface Area of a Trapezoid
The area of a trapezoid is calculated by taking the average of the lengths of the two parallel sides (bases) and multiplying by the height.
The formula is: Area = ½ × (base₁ + base₂) × height
Where 'base₁' and 'base₂' are the lengths of the parallel sides, and 'height' is the perpendicular distance between them.
Confusion between different quadrilateral types
Students often confuse the formulas for different quadrilaterals. Remember, each type has its own formula based on its properties.
Mistake 1
Incorrect measurement of sides
Ensure that you correctly identify which sides are the base, height, length, or width, depending on the type of quadrilateral.
Mistake 2
Using the wrong formula
Be careful to use the correct formula corresponding to the type of quadrilateral you are working with.
Mistake 3
Misidentifying the bases in trapezoids
In a trapezoid, only the parallel sides are considered bases. Make sure you use these in the formula.
Mistake 4
Forgetting to square the side in a square
When calculating the area of a square, make sure to square the length of the side, not just double it.
Mistake 5
Solved Examples of Surface Area of Quadrilateral
Find the area of a square with a side length of 8 cm.
Area = 64 cm²
Problem 1
Given side = 8 cm. Use the formula: Area = side² = 8 × 8 = 64 cm²
Find the area of a rectangle with a length of 10 cm and a width of 5 cm.
Explanation
Area = 50 cm²
Problem 2
Use the formula: Area = length × width = 10 × 5 = 50 cm²
A trapezoid has bases of 12 cm and 8 cm, and a height of 5 cm. Find the area.
Explanation
Area = 50 cm²
Problem 3
Use the formula: Area = ½ × (base₁ + base₂) × height = ½ × (12 + 8) × 5 = ½ × 20 × 5 = 50 cm²
Find the area of a rectangle with a length of 14 cm and a width of 3 cm.
Explanation
Area = 42 cm²
Problem 4
Use the formula: Area = length × width = 14 × 3 = 42 cm²
A square has an area of 81 cm². Find the length of one side.
Explanation
Side length = 9 cm
It is the total area covered by the quadrilateral's outer boundary.
1.What are the common formulas for quadrilateral areas?
2.What is the difference between a square and a rectangle?
3.How do you find the area of a trapezoid?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Quadrilateral
Students often make mistakes while calculating the surface area of quadrilaterals, 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
