# Triangles

## 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°

Two equal sides
Two equal angles

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:

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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:

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## 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: another 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":

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(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:

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