Find the area of a regular hexagon with apothem 2 square root 3mm. Round to the nearest whole number.

a 42mm^2

b 66mm^2

c 83mm^2

d 91mm^2

A = apothem, S = sidefor a hexagon: A = S / 2tan (30) = S / 0.577S = 0.577 * A recognize the triangle where the base is the side of the polygon, and the apothem is the heightThe area of this triangle is S*A/2 = 0.577 * A^2 / 2 we are given the value of A, so:the triangle area is 0.577 * (3√2) ^2 / 2 = 0.577 * 9 = 5.193 Finally, the area of the hexagon is the area of the triangle * 6

An apothem divide a hexagon into two 30-60-90 triangles and equilateral triangles.

what u just need to do is find side by using sin or cos or tan formula in that equilateral triangles.

as u get the side u can find the area, of a triangle.

and then u multiply it by 6 as there are 6 triangles.