Question
8
βFind the area of the regular polygon shown below and choose the appropriate result.
has 7 sides base is 4 and radious is 4.15
β
A
58 π258\ m^{2}58 m
2
B
58.1 π258.1\ m^{2}58.1 m
2
C
58.6 π258.6\ m^{2}58.6 m
2
D
58.5 π258.5\ m^{2}58.5 m
2
βFind the area of the regular polygon shown below and choose the appropriate result.
has 7 sides base is 4 and radious is 4.15
β
A
58 π258\ m^{2}58 m
2
B
58.1 π258.1\ m^{2}58.1 m
2
C
58.6 π258.6\ m^{2}58.6 m
2
D
58.5 π258.5\ m^{2}58.5 m
2
Answers
GPT 3.5
The formula for the area of a regular polygon is (perimeter x apothem) / 2.
The perimeter of the polygon can be calculated as 7 x 4 = 28 units.
The apothem can be found using the formula: apothem = radius / tan(180 / n), where n is the number of sides in the polygon. In this case, it is apothem = 4.15 / tan(180 / 7).
Calculating the apothem, we get approximately 5.89 units.
Now, we can find the area using the formula: (28 x 5.89) / 2 = 82.52 square units.
So, the correct answer is not provided in the options. The approximate area of the regular polygon is 82.52 square units.
The perimeter of the polygon can be calculated as 7 x 4 = 28 units.
The apothem can be found using the formula: apothem = radius / tan(180 / n), where n is the number of sides in the polygon. In this case, it is apothem = 4.15 / tan(180 / 7).
Calculating the apothem, we get approximately 5.89 units.
Now, we can find the area using the formula: (28 x 5.89) / 2 = 82.52 square units.
So, the correct answer is not provided in the options. The approximate area of the regular polygon is 82.52 square units.