# Apothem Length

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Apothem length in a triangle is the length calculated from a vertex of the triangle to the midpoint of the opposite side of the vertex. Apothem is always the perpendicular drawn from the vertex to the midpoint of the opposite side in the triangle. Similarly apothem in a circle is the length calculated from the center of the circle to the midpoint of the chord drawn in the circle.
Example 1: Find the length of the apothem in a triangle if a side of the triangle is 6m and area of the triangle is 45m2.

Given side length or base length of the triangle, b = 6m
Area of the triangle, A = 45m2

Formula to find the area of the triangle, A =1/2 * base length * apothem

Hence Area of the triangle, A: 45m2 = 1/2 * 6m * apothem
45 = 3 * apothem
In order to solve for apothem, we divide ‘3’ on both sides
Apothem = 45/3 = 15

Hence apothem of the given triangle = 15m

Example 2: Find the length of the apothem in a triangle if a side of the triangle is 4cm and area of the triangle is 24cm2.

Given side length or base length of the triangle, b = 4cm
Area of the triangle, A = 24cm2

Formula to find the area of the triangle, A =1/2 * base length * apothem

Hence Area of the triangle, A: 24cm2 = 1/2 * 4cm * apothem
24 = 2 * apothem
In order to solve for apothem, we divide ‘2’ on both sides
Apothem = 24/2 = 12

Hence apothem of the given triangle = 12cm