A triangle is a polygon with three sides.

There are several types of triangles which are based either on the length of the sides, or on the size of the angles. Here is how they are classified:

Classification based on Side Lengths:

  • Scalene = no sides equal in length
  • Isosceles = two sides equal
  • Equilateral = all three sides equal

Classification based on Angles:

  • Right = has one right (90º) angle
  • Acute = has three angles less than 90º
  • Obtuse = has one angle greater than 90º

Triangles can have more than one classification. For instance, you could make a right-isosceles triangle that has a 90º angle and two equal sides. Or you could have an obtuse-scalene triangle with an angle more than 90º and no equal sides.

To find the area of a triangle, think about the formula for the area of a rectangle. Essentially, a triangle is half the size of a rectangle if you cut in on a diagonal. Since the formula for a rectangle is L x W (length x width), we can just divide this by two to get the formula for the area of a triangle. The only difference for a triangle is that instead of calling the sides “length and width” we call them “base and height.” The base is the bottom of the triangle, and the height is how tall the triangle is (height must be perpendicular to the base).

Area of a triangle = (base x height) ÷ 2

Perimeter of a triangle = add all the sides

Example triangle math problems:

  1. If a triangle has a base of 6 cm, a height of 8 cm, and the third side is 10 cm, find the area and perimeter.
    • Use the formulas:
    • A = (b x h) ÷ 2
    • A = (6 x 8) ÷ 2 = 24 sq. cm
    • P = add all sides
    • P = 6 + 8 + 10 = 24 cm
    • For this triangle, A = 24 sq. cm, and P = 24 cm.
  2. A triangular garden is planted alongside a house. It has sides that are 9, 12, and 15 ft. 9 is the base and the side that is 12 ft. is alongside the house. How much fencing will it take to go around the garden, and what will the area of it be?
    • Let’s start with area:
    • A = (b x h) ÷ 2
    • A = (9 x 12) ÷ 2 = 54 sq. ft.
    • Now perimeter. The fencing around the garden is the perimeter in this scenario. However, no fencing is needed on one side since the house is there. We only have to add the two other sides:
    • P = 9 + 15 = 24 ft.
  3. What will the area be of a triangular garden with h = 3.5 ft and b = 6 ft.?
    • A = (b x h) ÷ 2
    • A = (6 x 3.5) ÷ 2 = 10.5 sq. ft.