A triangle is a three - sided convex polygon. The area of a triangle is actually found by manipulating a parallelogram. We know that the area of a parallelogram is found by taking the height and multiplying it by the base. If we construct a diagonal in the parallelogram, we find that we have actually created two congruent triangles.

In the following figure, triangle ABD is congruent to triangle CDB.

** AREA**-segment
BD has thus divided parallelogram ABCD into two congruent halves.
Therefore, if we take the area formula for the parallelogram,
Base x Height, and divide it in half as well, we are left with
the area of a triangle. Area = 1/2 x Base x Height.( The base
and the height are still perpendicular segments.)

We let the base be segment EF and height is segment GH. Therefore, the area would equal the product of these two segments divided by two.

** Problems**-
Solve the following problems involving triangles.

1) height = 5 in. , base = 6 in, find the area.

2) The area = 24 sq.m, height = 4 m, find the base.

3) The opening to a tent is 4.5 feet of the ground. The tent has a square bottom and the length between each ground stake is 8 feet. Find the amount of sleeping area in the tent and also the amount of space one has upon entering the tent.