What is the area of a hexagon with a apothem

Question

what is the area of a hexagone with a apothem of 23

Answer 1

assuming it's a regular hexagon...

there are 6 congruent triangles

the area of any one is given by the formula...

A=(a^2)tan(180/n) where a=apothem and n=number of sides or number of congruent triangles (6)

A=(23^2)tan(180/6)

A=529(tan 30º)

A=(529)(√3/3)

A=(529)(0.57735)

A=305.41815

there are 6 triangles

A=6*305.41815

A=1832.5089 square units