Triangles

A triangle has three sides and three angles

The three angles always add to 180°

Equilateral, Isosceles and Scalene

There are three special names given to triangles that tell how many sides (or angles) are equal.

There can be 3, 2 or no equal sides/angles:

Equilateral Triangle

Equilateral Triangle

Three equal sides
Three equal angles, always 60°

Isosceles Triangle

Isosceles Triangle

Two equal sides
Two equal angles

Scalene Triangle

Scalene Triangle

No equal sides
No equal angles


What Type of Angle?

Triangles can also have names that tell you what type of angle is inside:

Acute Triangle

Acute Triangle

All angles are less than 90°

Right Triangle

Right Triangle

Has a right angle (90°)

Obtuse Triangle

Obtuse Triangle

Has an angle more than 90°


Combining the Names

Sometimes a triangle will have two names, for example:
Right Isosceles Triangle

Right Isosceles Triangle

Has a right angle (90°), and also two equal angles

Can you guess what the equal angles are?

Play With It ...

Try dragging the points around and make different triangles:


View Larger

You might also like to play with the Interactive Triangle.

Perimeter

The perimeter is the distance around the edge of the triangle: just add up the three sides:

Area

triangle b h

The area is half of the base times height.

  • "b" is the distance along the base
  • "h" is the height (measured at right angles to the base)
Area = ½ × b × h

The formula works for all triangles.

Note: another way of writing the formula is bh/2

Example: What is the area of this triangle?

Triangle

(Note: 12 is the height, not the length of the left-hand side)

 

Height = h = 12

Base = b = 20

Area = ½ × b × h = ½ × 20 × 12 = 120

The base can be any side, Just be sure the "height" is measured at right angles to the "base":

(Note: You can also calculate the area from the lengths of all three sides using Heron's Formula.)

Why is the Area "Half of bh"?

Imagine you "doubled" the triangle (flip it around one of the upper edges) to make a square-like shape (it would be a "parallelogram" actually), THEN the whole area would be bh (that would be for both triangles, so just one is ½ × bh), like this:

triangle area
By slicing the new triangle and moving the sliced part to the other side
you get a simple rectangle, whose area is bh.