The regular hexagon has a radius of 4 in. what is the approximate area of the hexagon? 24 in.2 42 in.2 48 in.2 84 in.2

The central angle of a hexagon is 60°. Dividing it by two will give us 30°. The side opposite to 30° is 2 inches, multiplied by 2 is 4 inches. Thus, each side of the hexagon is 4 inches. Also, the apothem is 2sqrt(3). The area of the figure is calculated through the equation,
                                           A = 0.5aP
where a is apothem and P is perimeter
Substituting,
                                           A = 0.5(2sqrt3)(4 x 6) = 24sqrt3
The answer is approximately 41.57 in².

The question is kind of confusing. if it's asking how many variations of answers can you give. then do 4^5 for your answer.this would be something like the first question could be a and the 2nd c or first b next c etc. if you can, ask the teacher for a better confirmation of what it's asking. if i'm assuming correctly what it's asking, it's 625 different variations.