Question

An equilateral triangle has an apothem of 5 cm. Find the perimeter of the triangle to the nearest centimeter.

Answer 1

The apothem is the distance from the center to the midpoint of one of the sides of a regular polygon. You can make a right triangle with the apothem, the line from the midpoint to the corner and the line from the center to the corner. An equilateral triangle has 60 degree angles (180/3). The right triangle has half of one of those angles so 30 degrees. Now we have a 30-60-90 triangle where the short leg is 5cm. The long leg, which is also half of one side of the triangle is thus
`5√(3)`. A whole side of the triangle is
`10√(3)`. Multiply that by 3 to get the perimeter of
`30√(3)`.