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

Three equal sides

Three equal angles, always 60°

Isosceles Triangle

Two equal sides

Two equal angles

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

All angles are less than 90°

Right Triangle

Has a right angle (90°)

Obtuse Triangle

Has an angle more than 90°

Combining the Names

Sometimes a triangle will have two names, for example:

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:

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

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: a simpler way of writing the formula is bh/2

Example: What is the area of this 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 (a parallelogram) which can be changed to a simple rectangle:

THEN the whole area is bh, which is for both triangles, so just one is ½ × bh.