SOLUTION: Exam: Geometry Exam 4 E (Copy) Assume that Hexagon ABCDEF is a regular polygon, all angles that look like right angles are, and that the perimeter is 120 units.

Question 193357This question is from textbook
: Exam: Geometry Exam 4 E (Copy)

Assume that Hexagon ABCDEF is a regular polygon, all angles that look like right angles are, and that the perimeter is 120 units.

17. What is the area of hexagon ABCDEF?

A.
259.8 square units

B.
519.6 square units

C.
1039.2 square units

D.
2078.4 square units

This question is from textbook

Found 2 solutions by RAY100, solver91311:
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
please restate problem, if a regular hexagon, apothem =5.774, and area is 346.44
perhaps mention of "right angles" cause this not to be a regular hexagon

Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!

If you have a regular hexagon with a perimeter of 120, then each side must measure 120 divided by 6 or 20. A regular hexagon is composed of 6 equilateral triangles whose sides are equal in measure to one of the sides of the hexagon. So calculate the area of an equilateral triangle with side length of 20 and multiply by 6.

The area of a triangle is given by:

The base of an equilateral triangle is just the length of any of the sides, and the height of an equilateral triangle forms a 30-60-90 right triangle where the hypotenuse is the length of one side, the short leg is half of the length of one side, and the long leg (and the measure of the height) is the length of one side of the equilateral triangle times the square root of 3. Therefore the area of the equilateral triangle is:

And the area of the hexagon is:

Plug in the value for s and do the arithmetic.

John