The perimeter of a triangle is the sum of the lengths of all three sides.
In this triangle, the perimeter is: 5 + 6 + 10 = 21. This is a relatively simple property of a triangle, so often it will be used in combination with another property. Try this next problem. What is the perimeter of triangle PQR?
To solve for the perimeter, you will need to determine the value of x. Because angles QPR and PRQ are both 50°, you know that their opposite sides will have equal lengths. That means sides PQ and QR must have equal lengths, so you can infer that side QR has a length of 9. The perimeter of triangle PQR is: 9 + 9 + 12 = 30.
Find the perimeter of each triangle.
Note: Figures not drawn to scale.
You need to be ready to solve geometry problems without depending on exactly accurate figures.
The final property of a triangle to review is area. You may be familiar with the equation
.
One very important thing to understand about the area of a triangle (and area in general) is the relationship between the base and the height. The base and the height MUST be perpendicular to each other. In a triangle, one side of the triangle is the base, and the height is formed by dropping a line from the opposite point of the triangle straight down toward the base, so that it forms a 90° angle with the base. The small square located where the height and base meet (shown in the following figure) is a very common symbol used to denote a right angle.
An additional challenge on the GRE is that problems will ask you about familiar shapes but present them to you in orientations you are not accustomed to. Even the area of a triangle can be affected. Most people generally think of the base of the triangle as the bottom side of the triangle, but, in reality, any side of the triangle could act as a base. In fact, depending on the orientation of the triangle, there may not actually be a bottom side. The following three triangles are all the same triangle, but each one has a different side as the base, and the corresponding height is drawn in.
As it turns out, not only can any side be the base, but the height might be drawn outside the triangle! The only thing that matters is that the base and the height are perpendicular to each other.
Determine the areas of the following triangles.
