Answer:
b) 41.6 square inches
Explanation:
A regular hexagon is inscribed in a circle with a diameter of 8 inches.
Step 1
We find the radius
Radius = Diameter/2
= 8 inches/2 = 4 inches
a. What is the perimeter of the hexagon?
b. What is the area of the hexagon?
An hexagon has 6 sides
The number of angles in an hexagon is calculated as:
[(Number of sides - 2) x 180]
= (6 - 2) x 180 = 720 ÷ 6 = 120°
The hexagon into 6 equilateral triangles with 4 for each of its sides.
The area of one of the triangles:
Height = 2√3
- one triangle's area = (1/2)bh = (1/2)(4)(2√3) = 4√3
The area of the hexagon by multiplying the one triangle's area by 6:
6 x 4√3 = 24√3 square inches
= 41.569219382 square inches
Approximately = 41.6 square inches