Triangle

The angles in a triangle add up to 180°.

Pythagoras' theorem states that in a right triangle (or right-angled triangle) the sum of the squares of the two smaller sides of the triangle is equal to the square of the hypotenuse.

a^2 + b^2 = c^2

where c is the hypotenuse (the longest side) and a and b are the other sides of the right triangle.

To find the area of a triangle
The area of a triangle is equal to half of the base multiplied by the perpendicular height of the triangle.

The Area of a triangle is 1/2 x base (b) x height (h) = 1/2bh

Formula for Area of Scalene Triangle :
= ?[s(s - a)(s - b)(s - c)]

where
S = (a + b + c) / 2

Here a, b and c are side lengths of the triangle.

Formula for Area of Equilateral Triangle :
= (?3/4)a2

To find the perimeter of a triangle
The perimeter of a triangle is the sum of all its three sides. We can work out the perimeter using the following formula: Perimeter of a triangle = sum of all three sides. If a, b and c are the sides of the triangle, then. Perimeter of triangle = a + b + c

To find the altitude in a triangle
A right triangle is a triangle with one angle equal to 90°. Two heights are easy to find, as the legs are perpendicular: if the shorter leg is a base, then the longer leg is the altitude (and the other way round). The third altitude of a triangle may be calculated from the formula: h? = area * 2 / c = a * b / c

Heron's Formula:
Heron was born in about 10AD in Alexandria in Egypt. His work on mathematical and physical subjects is so numerous and varied that he is considered to be an encyclopedia writer in these field. His geometrical work deals largely with problems on mensuration.

The formula given by Heron is a famous formula for calculating area of a triangle in terms of its three sides.
Let a b and c are the sides of the triangle and s is semi perimeter i.e. s = a + b + c 2
This formula can be used for any triangle to calculate its area and it is very useful where it not possible to find the height of the triangle easily.

Theorem: Two triangles on the same base (or equal bases) and in between the same parallels are equal in area.
Here, ar(â–³ABC) = ar(â–³DBC)
Theorem: The area of a triangle is half the product of its base (or any side) and the corresponding altitude (or height).
Here, area(ABC) = 1/2 × base × height.



Basic Triangle Trigonometry
In basic triangle trigonometry, we look at three trigonometric functions: sine, cosine and tangent (sin, cos and tan) with right triangles.

? is one of the angles of the right triangle (but not the right angle!)
h is the hypotenuse - the longest side of the right triangle
o is opposite to the angle
a is adjacent to the angle

The three formulas to rememeber can be summed up in one acronym:

SOH CAH TOA
where s stands for sine, c for cosine and t for tangent.