Surface Area of Quadrilateral
2026-02-28 09:12 Diff
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Last updated on August 30, 2025

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.

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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.

Problem 1

Given side = 8 cm. Use the formula: Area = side² = 8 × 8 = 64 cm²

Okay, lets begin

Find the area of a rectangle with a length of 10 cm and a width of 5 cm.

Explanation

Area = 50 cm²

Well explained 👍

Problem 2

Use the formula: Area = length × width = 10 × 5 = 50 cm²

Okay, lets begin

A trapezoid has bases of 12 cm and 8 cm, and a height of 5 cm. Find the area.

Explanation

Area = 50 cm²

Well explained 👍

Problem 3

Use the formula: Area = ½ × (base₁ + base₂) × height = ½ × (12 + 8) × 5 = ½ × 20 × 5 = 50 cm²

Okay, lets begin

Find the area of a rectangle with a length of 14 cm and a width of 3 cm.

Explanation

Area = 42 cm²

Well explained 👍

Problem 4

Use the formula: Area = length × width = 14 × 3 = 42 cm²

Okay, lets begin

A square has an area of 81 cm². Find the length of one side.

Explanation

Side length = 9 cm

Well explained 👍

It is the total area covered by the quadrilateral's outer boundary.

1.What are the common formulas for quadrilateral areas?

Common formulas include those for squares, rectangles, and trapezoids, each with its specific calculation method.

2.What is the difference between a square and a rectangle?

A square has all sides equal, while a rectangle has opposite sides equal and all angles are right angles.

3.How do you find the area of a trapezoid?

Calculate the average of the lengths of the bases and multiply by the height.

4.What unit is surface area measured in?

Surface area is always measured in square units like cm², m², or in².

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.

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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