How To Calculate Area Of Triangles

 

Mathematics is full of fascinating shapes, but one of the most fundamental shapes you will ever encounter is the triangle. Whether you are looking at the roof of a house, a slice of pizza, or a yield traffic sign, triangles are everywhere!

In this post, we will define what a triangle is, explore its four primary types with visual diagrams, and solve 5 simple practice questions perfect for primary school students.

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What is a Triangle?

A triangle is a closed, three-sided geometric shape. It is formed by connecting three straight line segments. Every triangle has exactly:

• 3 sides (the straight edges)
• 3 vertices (the corner points where the sides meet)
• 3 internal angles (the space inside the corners)

Fun Fact: No matter how big or small a triangle is, the sum of its three internal angles always adds up to exactly 180°.

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The Four Main Types of Triangles

Triangles are generally classified by the lengths of their sides or the sizes of their angles. Here is how the four main types look and differ from one another:

Equilateral
All sides equal

Isosceles
2 sides equal

Scalene
No sides equal

Right-Angled
One 90° angle

1. Equilateral Triangle

An equilateral triangle is a triangle where all three sides are equal in length. Because the sides are equal, all three internal angles are also equal, each measuring exactly 60°.

2. Isosceles Triangle

An isosceles triangle has two sides of equal length and one side that is different. The angles opposite to the equal sides are also equal to each other.

3. Scalene Triangle

A scalene triangle is a triangle where all three sides have different lengths. Consequently, all three internal angles have different measurements as well.

4. Right-Angled Triangle

A right-angled triangle (or right triangle) is a triangle that has one internal angle that measures exactly 90° (called a right angle). The side opposite the right angle is always the longest side, known as the hypotenuse.

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How to Calculate the Area of a Triangle

To find out how much space is inside a triangle, you just need to know two measurements: the Base (the bottom side) and the Height (the straight vertical distance from the top point down to the base).

← ——— Base (B) ———→

The formula is:

Area = ½ × Base × Height

Or simply: Multiply the base by the height, and then divide the answer by 2.

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5 Simple Questions and Solutions for Primary School

Question 1

Find the area of a triangle with a base of 6 cm and a height of 4 cm.

Solution:

• Base = 6 cm, Height = 4 cm
• Area = ½ × Base × Height
• Area = ½ × 6 × 4
• Area = ½ × 24
• Answer: Area = 12 cm²

Question 2

A triangular biscuit has a base of 8 cm and a height of 5 cm. What is its area?

Solution:

• Base = 8 cm, Height = 5 cm
• Area = ½ × 8 × 5
• Area = ½ × 40
• Answer: Area = 20 cm²

Question 3

A right-angled triangle has a base of 10 cm and a height of 3 cm. Calculate its area.

Solution:

• Base = 10 cm, Height = 3 cm
• Area = ½ × 10 × 3
• Area = 5 × 3
• Answer: Area = 15 cm²

Question 4

The base of a triangle is 12 cm and its height is 6 cm. Find the area.

Solution:

• Base = 12 cm, Height = 6 cm
• Area = ½ × 12 × 6
• Area = 6 × 6
• Answer: Area = 36 cm²

Question 5

A small triangular flag has a height of 7 cm and a base of 4 cm. What is the area of the flag?

Solution:

• Base = 4 cm, Height = 7 cm
• Area = ½ × 4 × 7
• Area = 2 × 7
• Answer: Area = 14 cm²

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Parents and Teachers: Feel free to change the numbers in these questions to give your children more practice! Happy learning!