08Ztriangles

toc = Area of Triangles =

Basic Rule
{Use this rule when you know the base and height of the triangle}


 * Demonstration **

The blue triangle is enclosed in a rectangle with
 * width = base of triangle (and)
 * height = height of triangle

So Area(rectangle) = base × height

It should be clear that
 * Area A = Area A'
 * Area B = Area B'

So Area(triangle) = ½ × Areas(rectangle) So Area(triangle) = ½ × base × height


 * Example 1 **



Heron's Formula
(also called Hero's Formula)

{Use this rule when the lengths of three sides of the triangle are known}

{NB: the rule is symmetrical so it does not matter which side is named a, b or c}


 * Example 2 **



<< Extension for Year 10 >>

Area using Trigonometry
{Use this rule when you know two sides and the angle __between__ them}




 * Example 3 **




 * Proof of the Sine Rule for Area of a Triangle **



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