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:
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°
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Right Triangle
Has a right angle (90°)
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Obtuse Triangle
Has an angle more than 90°
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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? |
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.
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Area = ½ × b × h
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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"
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:
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By slicing the new triangle and moving the sliced part to the other side you get a simple rectangle, whose area is bh. |