The area of a triangle is half the product of its base and height. But did you know where did the formula come from? Let us discuss it in this post.
The area of a triangle is related to the area of other shapes, but we are going to relate it to the area of a parallelogram.
Consider the triangle above with base and height . If we are going to create another triangle congruent to it (congruent means the same size and shape), then we can form a quadrilateral by coinciding their two corresponding sides. What is interesting is that every time we do this, we create a parallelogram.
Now, we have already learned that getting the area of a parallelogram is multiplying the base and the height . So,
However, in calculating the area of the parallelogram above, we actually calculated for the areas of two triangles. This means that to get the area of the original triangle, we have to divide by 2.
Therefore, the area of a triangle is
That is the reason behind the formula. Now let’s have a worked example.
Find the area of a triangle with base 12 units and height 8 units.
From the derivation above,
What is the height of a triangle with area 14 square units and base 4 units.
Again, we use the original formula above and substitute the values?
Dividing both sides by 2 gives us
In the next post, we are going to discuss more examples on problems involving area of triangles.