Lesson 15 — Activity 3: Estimating and Calculating the Area of Triangles

Getting Ready

A triangle is a closed two-dimensional shape consisting of three straight sides. In this activity, you will estimate and calculate the area of triangles.

This image shows examples of triangles.

Estimating the Area of Triangles

The area of a triangle can be estimated using a variety of methods. One method is to use dot paper.

This image shows how to estimate the area of a triangle.

Count the number of whole squares inside the shape. The triangle above has one whole square. Combine partial squares to make whole squares. The triangle has two partial squares that combine to make one whole square.

Try This:

Estimate the area of the following triangle. Remember to count the number of whole squares, then combine partial squares to make whole squares. Write your answer as in the above example.

     Estimate the area of this triangle.      

10 whole squares  = 10 units2
5 partial squares =   2.5 units2
Total area               =  12.5 units2

Calculating the Area of Triangles

If you fold a square or a rectangle in half diagonally, you can make two triangles. Take some paper and try this.

This image shows triangles made from folding squares and rectangles.

Therefore, the area of a triangle must be half the area of a square or rectangle.

The formula for calculating the area of a triangle is:

Area of a triangle formula                                                                        

Let's say you had a triangle with a base that was 14 mm long and a height that was 17 mm. You could calculate the area like this:

Image 1

A = 14 x 17


A = 119 mm2

Try This:

Calculate the area of the triangles below. Follow the formula above.

1.Image 2             2.   Image 2

1.  A = 4 x 3 

    A = 6 mm2

2.  A = 5 x 6 

     A = 15 cm2

Images courtesy of www.imagesgoogle.com and K&E Studio