# A Guide to the GRE/Areas of Triangles

## Areas of Triangles

The area of a triangle equals half of the base multiplied by the height.

In a right triangle, the base and the height will be the two smallest sides.

The area of this triangle equals (6)(8) divided by 2, or 24, because in a right triangle the base and the height are the two smaller sides

Otherwise, however, the height of the triangle will have to be known or deduced.

The height of an isosceles triangle can be deduced using the Pythagorean Theorem.

Take the original triangle. Split the base in half. The height will be perpendicular.

Under the Pythagorean Theorem:

The larger side squared equals the sum of the other sides squared.

Expand the exponents.

Subtract 25 from both sides.

Take the square root of both sides. The triangle has a height of 12 and thus an area of 30.

### Practice

1.

What is the area of the triangle?

2.

What is the area of this triangle expressed in terms of s and t

3.

What is the area of the triangle?