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.

Area of a triangle
When you know the lenght of the base and the height, you can use the formula:

Area= $\frac{1}{2}$ ·b·h, where b is the base and h is the height

Find the area of an acute triangle with a base of 15 inches and a height of 6 inches.

Area= $\frac{1}{2}$ ·b·h

Area= $\frac{1}{2}$ ·(15 in)·(6 in)

Area= $\frac{1}{2}$ ·90 in²

Area=45 in²

Area of a triangle (Heron's Formula)
Heron's formula 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 = $\frac{a+b+c}{2}$ , then:

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

Find the area of triangle from a = 4, b = 6 and c = 4 using heron's formula.

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

s = $\frac{a+b+c}{2}$ = $\frac{4+6+4}{2}$ = 7

$Area=\sqrt{s(s-a)(s-b)(s-c)}$ = $\sqrt{7(7-4)(7-6)(7-4)}$ = 7.94

Find the area of the triangle where:
the height is 4 and the base is three times the height

Area=