Find the area of a regular hexagon with the given measurement. 48-inch perimeter

Question

Radical form needed. I really need. Help.

Answer 1

a hexagon has 6 sides

each side = 48/6 = 8 inches

divide the hexagon into 3 parts

a rectangle in the middle with one side = 8

two triangles on either side of the rectangle, each with 2 sides = 8

each interior angle of a hexagon = 120 degrees

the triangles on either side of the rectangle have angles 120, 30 and 30 degrees

divide that 120, 30, 30 triangle into two triangles with angles 60,90 and 30 each

with sides 8, 4 and 4sqr3

its area = (1/2)4(4sqr3) = 8sqr3

there are 4 such triangles with total area 32sqr3

the rectangle has dimensions 8 by 8sqr3 with area 64sqr3

total area of the hexagon = 64sqr3 + 32sqr3 = 96sqr3 in^2

Area of a hexagon = Perimeter times 2sqr3 = 48 x 2sqr3 = 96sqr3