Area of a Triangle

We have moved onto area of a triangle.  The concept remains the same: area means "what is covered" by an object.  Since a triangle is a different object, we will have a different formula.

Any triangle is half of a larger rectangle.

The triangle is on the left.  The dashed lines on the right triangle represent a hypothetical rectangle

The formula for AREA OF A RECTANGLE is a = l x w.

This can lead us to the area of a triangle by dividing the area of a rectangle by 2.

a = l x w ÷ 2

With triangles, we don't call it length and width.  We call it the base and the height, so we can change l and w to b and h.

a = b x h ÷ 2

The official formula for AREA OF A TRIANGLE is

a = 1/2 b x h

Here is a labeled triangle. The base and the height always create a right angle from perpendicular lines.

We are beginning to remove the x for multiply, so our formula would look like this

a = 1/2bh

Symbols touching or numbers touching symbols means to multiply.

Let's look at an example:

We will then use our formula:

a = ?                                              a = 1/2 (5) (6)   since parentheses means multiply ( 5 x 6 )

b = 5 in                                           a = 1/2 (30)       then 1/2 x 30

h = 6 in                                           a = 15 in^2          the ^ means exponent, or to the power of

                                                  (read 15 inches squared or 15 square inches)

Below is another example worked out on the marker board.  We used our knowledge of multiplying fractions.

Click here for help with multiplying fractions.

One final note:  the height isn't always inside the triangle.  Sometimes you have to draw it outside.  Also, any side can be a base as long at there is a perpendicular line drawn from base to the opposite vertex, or corner.