Area of a triangle

Teaser and introduction goes here. Sample problem here.

 How do we find the area of a triangle? It would be difficult to count the unit squares inside this triangle, since many of the squares have been cut into fractional parts by the sides of the triangle. So we need to find a sneaky way of counting all the squares inside the triangle.

To do this, let’s double the area or the original triangle by adding a second triangle to the figure to create a parallelogram.

We have learned that multiplying the base and height of a parallelogram gives the area of the parallelogram, so the area of this parallelogram is 6 • 4 = 24 square units. Since we only needed the area of the triangle, we divide 24 by 2 to get the area of the triangle, which is 12 square units.

To put all this in one line, it would look like this:

Area = (area of parallelogram) ÷ 2= (base • height) ÷ 2 = (6 • 4) ÷ 2 = 12 u^2

More often, the formula for the area of a triangle is written as

A = $\large~\frac{bh}{2}$

Where b and h is the base and height of the triangle, respectively.

 Find the area of this triangle. A = $\large~\frac{bh}{2}=\frac{6•3}{2}=\frac{18}{2}=9\,u^2$

 Find the area of this triangle. A = $\large~\frac{bh}{2}=\frac{7•4}{2}=\frac{28}{2}=14\,u^2$

 Directions: Move the blue vertices to create a triangle. Use the "Hint 1" slider to see how a triangle compares with a parallelogram. Use the "Hint 2" slider to see how to calculate the area of the triangle.

Self-Check

 Question 1 Find the area of this triangle. [show answer] A = $\large~\frac{bh}{2}=\frac{7•5}{2}=\frac{35}{2}=17.5\, u^2$

 Question 2 Find the area of this triangle. [show answer] A = $\large~\frac{bh}{2}=\frac{2•5}{2}=\frac{10}{2}=5\, u^2$

 Question 3 Find the area of this triangle. [show answer] A = $\large~\frac{bh}{2}=\frac{3•5}{2}=\frac{15}{2}=7.5 \,u^2$