• Know how to use basic formulas for area and perimeter of a triangle. The area is A = ½bh where b is the length of the base of the triangle and h is the altitude to that base. The perimeter is found by adding the lengths of the three sides.
• Solve basic linear and quadratic equations.
• Use the Pythagorean Theorem in finding the length, width, and hypotenuse of a right triangle.
• Know the formulas for the height and area of an equilateral triangle where s is the length of one side: and .
• Know basic trig functions and how to use them in a right triangle.

Suppose in a right triangle one of the legs is of length 5 and the angle formed by the hypotenuse and this leg is 28°. What are the area and perimeter of this triangle? A diagram is shown below.

 

 

A right triangle is a special case of this type of problem since the legs are perpendicular. One leg is the base and the other is the height or altitude of the triangle. In order to find h in the diagram above we use

 

h » 2.6585

 

We can now find the area from

 

 A = (1/2)bh = (1/2)(5)(2.6585) = 6.64625

 

To find the perimeter, we need the hypotenuse so we can add all three sides. We find the hypotenuse using the Pythagorean Theorem:

 

 

We add the lengths of the three sides and get

 

perimeter = 13.3213

 

Suppose a triangle with area 28 has a base of 7x and a height of 4x as shown in the diagram below. What are the area, the perimeter, and the dimensions of this triangle?

 

 

We know area is 28 and equals ½bh. We write

 

 

Next we solve the equation 28 = 14x² for x

 

x =

 

We now know that

 

 

We can check our work by recalculating the area

 

A =

 

The frustrating part of this analysis is that we cannot find the measures of the other two sides with the information that we have been given. Therefore, we can solve for x, and get the lengths of the altitude and base, but we will never be able to determine either the dimensions or the perimeter of this triangle.