How to Find the Area of a Triangle

Geometry is a branch of mathematics that deals with the measurement, relation and properties of solids, lines, points and angles. One of the basic shapes in our world is the triangle. Finding the area of a triangle is an important skill for all kinds of people including engineers, mathematicians and students.

Instructions

1. Take a piece of paper and draw a rectangle. Draw a diagonal line from one corner across the area of the rectangle to the other end. The area of the rectangle is the length times the width. The area of each right triangle is 1/2 x length x width.

2. Sketch a fresh new rectangle. Do not draw a right triangle this time; but draw two lines from each corner of the base, or bottom length, of the rectangle that meet at the top of the rectangle. You just drew a triangle that has three acute angles.

3. Notice how the formula, base x height x 1/2, once again gives the area of the triangle. This time, however, you divided the rectangle into three triangles. The area of the two smaller triangles added together equals the area of the larger triangle that you just calculated above by b x h x 1/2.

4. Calculate the area of an obtuse triangle now. So far, we found the area for a right triangle, then for a triangle with three acute angles. Now we are going to find the area for an obtuse triangle.

5. Make one side of the obtuse angle the base--choose one of the shorter sides for this exercise (but you can choose any side as the base to find area). Draw a dotted or imaginary line out from the base, extending the base line. Now draw a dotted or imaginary straight vertical line down from the highest point of the triangle to the imaginary base.

6. See how the extended lines and the obtuse triangle together form a right triangle. Continue with line extensions to make a rectangle out of the shape. You can see how the obtuse triangle and the first extensions form one-half of a rectangle.

7. Examine the formula for the base x height x 1/2 and apply it to the obtuse triangle alone and you get the area of the obtuse triangle. Take the base x the height x 1/2 of the imaginary extended right triangle to the obtuse and you get its area too. These two triangle areas added together equal that of one-half of the rectangle made by imaginary extended lines. Try it!