How to Find the Area of a Triangle (Mathematics Lesson)
How to Find the Area of a TriangleThe area of a triangle is found using the formula:
In this formula, b is the length of the base of the triangle and h is the height of the triangle. The image below shows what we mean by the lengths of the bases and the height:
A Real Example of How to Find the Area of a Triangle
An Example QuestionWhat is the area of a triangle with a base of 5 cm and a height of 3 cm, as shown below?
Step 1Start with the formula:
Area = ½bhDon't forget: ½bh = ½ × b × h
Step 2Substitute the length of the base and the height into the formula. In our example, b = 5 and h = 3.
Area = ½ × 5 × 3 = 7.5 cm2Don't forget: ½ × a number = 0.5 × a number = a number ÷ 2.
The area of the triangle with a base of 5 cm and a height of 3 cm is 7.5 cm2.
Another Real Example of How to Find the Area of a TriangleThe slider below shows another real example of how to find the area of a triangle:
How to Find the Area of a Triangle Using TrigonometryThe area of a triangle can also be found using trigonometry.
The area is found using the formula:
In the formula, a and b are lengths of two sides of the triangle and C is the angle between them. The image below shows what we mean by the two sides and the angle between them:
Read more about how to find the area of a triangle using trigonometry
Here's a second test on finding the area of a triangle.
Here's a third test on finding the area of a triangle.
What Is a Triangle?A triangle is a flat shape with three straight sides and three corners (also called vertices).
There are different types of triangle:
What's in a Name?A triangle has three corners and so three angles.
Just as a tricycle has three wheels, and a tripod has three legs, a shape with three angles in called a triangle.
Areas of Triangles and RectanglesThe area of a triangle is ½bh.
The area of a rectangle is bh.
The area of the triangle is half that of the rectangle with the same base length and height.
Can you see from the image of a right-angled triangle below that this is the case?
What about this triangle below?