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101 LearnersLast updated on September 4, 2025
Surface Area of Triangle
A triangle is a 2-dimensional shape with three sides and three angles. The surface area of a triangle refers to the region enclosed by its three sides. In this article, we will learn about the surface area of a triangle, including various types of triangles and their respective area formulas.
What is the Surface Area of a Triangle?
The surface area of a triangle is the total area enclosed by its three sides. It is measured in square units.
A triangle is a 2-dimensional shape with three vertices and three edges.
Triangles can be classified into different types based on their sides and angles, such as equilateral, isosceles, and scalene triangles. Each type of triangle has a specific method to calculate its area.
Surface Area of a Triangle Formula
Triangles can have different area calculation formulas based on their type and given dimensions.
The most common method is using the base and height of the triangle. Here's an overview of some important formulas:
Area of a Triangle Using Base and Height
The area of a triangle can be calculated using its base and height with the formula: Area = (1/2) × base × height
Here, the base is any side of the triangle, and the height is the perpendicular distance from the base to the opposite vertex.
Area of a Triangle Using Heron's Formula
When the lengths of all three sides of a triangle are known, Heron's formula can be used to find the area.
The formula is as follows: Area = √[s(s-a)(s-b)(s-c)]
Where a, b, and c are the lengths of the sides, and s is the semi-perimeter of the triangle, calculated as: s = (a+b+c)/2
Area of an Equilateral Triangle
For an equilateral triangle, where all sides are equal, the area can be calculated using the formula:
Area = (√3/4) × side²
This formula uses only the length of one side to calculate the area.
Confusion between Different Formulas
Students might confuse the formulas for different types of triangles or different methods of calculation. Always ensure you know which formula applies to the given triangle.
Mistake 1
Misidentifying Base and Height
Some students mistakenly identify the wrong side as the base or miscalculate the height. Remember, the height is always perpendicular to the base.
Mistake 2
Incorrect Use of Heron's Formula
In using Heron’s formula, students often make arithmetic errors in calculating the semi-perimeter or fail to apply the square root correctly. Double-check calculations to avoid these mistakes.
Mistake 3
Using Incorrect Units
Ensure that all measurements are in the same unit before calculating the area. The area should be expressed in square units.
Mistake 4
Neglecting the Type of Triangle
Different triangles require different formulas. Make sure to apply the correct formula for the given type of triangle, such as equilateral or scalene.
Mistake 5
Solved Examples of Surface Area of Triangle
Find the area of a triangle with a base of 8 cm and a height of 5 cm.
Area = 20 cm²
Problem 1
Using the formula: Area = (1/2) × base × height = (1/2) × 8 × 5 = 4 × 5 = 20 cm²
Calculate the area of a triangle with sides measuring 7 cm, 8 cm, and 9 cm.
Explanation
Area = 26.83 cm²
Problem 2
First, find the semi-perimeter: s = (7+8+9)/2 = 12 Using Heron's formula: Area = √[s(s-a)(s-b)(s-c)] = √[12(12-7)(12-8)(12-9)] = √[12 × 5 × 4 × 3] = √720 = 26.83 cm²
Find the area of an equilateral triangle with a side length of 6 cm.
Explanation
Area = 15.59 cm²
Problem 3
Using the formula for an equilateral triangle: Area = (√3/4) × side² = (√3/4) × 6² = (√3/4) × 36 = 15.59 cm²
Calculate the area of a triangle with a base of 10 cm and height of 12 cm.
Explanation
Area = 60 cm²
Problem 4
Using the formula: Area = (1/2) × base × height = (1/2) × 10 × 12 = 5 × 12 = 60 cm²
A triangle has sides of 5 cm, 12 cm, and 13 cm. Find its area using Heron's formula.
Explanation
Area = 30 cm²
It is the total area enclosed by the three sides of a triangle, measured in square units.
1.What are common methods to find the area of a triangle?
2.What is the difference between base and height?
3.Can Heron's formula be used for any triangle?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Triangle
Students often make mistakes while calculating the area of a triangle, which leads to incorrect 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
