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2-D Shapes
Triangle

A triangle is a figure formed when three noncollinear points are connected by segments.

Each pair of segments forms an angle of the triangle. The vertex of each angle is a vertex of the triangle.

The sum of the measures of the angles of a triangle
is 180.

The sum of the lengths of any two sides of a triangle must be greater than the third side. That is:

a + b > c
a + c > b
b + c > a

The subtraction of the lengths of any two sides of a triangle must be smaller than the third side.

Triangles can be classified by:

Their sides:
 Equilateral Isosceles Scalene All three sides have equal lengths Exactly two equal sides All sides have different lengths

Their angles:

 Acute Right Obtuse All interior angles are acute (<90º) One angle is a right angle (90º) One angle is obtuse (>90º)

Area of a triangle

There are several ways to compute the area of a triangle:

1. When you know the lenght of the base and the height, you can use the formula:
$Area=\frac{1}{2}\;b\;\cdot\;h\;where\;b\;is\;the\;base\;and\;h\;the\;height$

2. Another is Heron's formula which gives the area in terms of the three sides of the triangle:
Suppose we know the values of the three sides a, b and c of the triangle.
If s is the semiperimeter of the triangle, that is, s = (a + b + c)/2, then:

$Area=\sqrt{s(s-a)(s-b)(s-c)}$

Find the area of the triangle where:
the height is 2 and the base is three times the height
Area=