Question

The area of the regular hexagon is 50 in sq. What is the measure of the apothem?

A) 10 in
B) 5 in
C) 25 in
D) 2 in

Answer 1

To find the measure of the apothem of a regular hexagon, use the formula: Area = (1/2) * apothem * perimeter. Substitute the area value and solve the equation to find the apothem.

Step-by-step explanation:

To find the measure of the apothem of a regular hexagon, we need to use the formula:

Area = (1/2) * apothem * perimeter

Given that the area of the hexagon is 50 sq in, we can substitute this value into the formula:

50 = (1/2) * apothem * perimeter

Since a regular hexagon has six equal sides, the perimeter is 6 times the length of one side. So, the equation becomes:

50 = (1/2) * apothem * 6 * side

We also know that the side length of the hexagon can be found using the formula:

Side = 2 * apothem * tan(180/6)

Substituting the value of the side length into the previous equation, we get:

50 = (1/2) * apothem * 6 * (2 * apothem * tan(180/6))

Simplifying this equation will give us the value of the apothem.

Therefore, to find the measure of the apothem of the hexagon, you can solve the equation.