Answer :
The Answer is B: 2,125 cm²
n = 7
a = 24.18 cm
r = 25.1051 cm
R = 27.8646 cm
A = 2124.65 cm²
P = 169.26 cm
x = 128.571 °
y = 51.4286 °
Agenda:
r = inradius (apothem)
R = circumradius
a = side length
n = number of sides
x = interior angle
y = exterior angle
A = area
P = perimeter
π = pi = 3.14159...
√ = square root
Formula: A = (1/4)na2 cot(π/n) = nr2 tan(π/n)
n = 7
a = 24.18 cm
r = 25.1051 cm
R = 27.8646 cm
A = 2124.65 cm²
P = 169.26 cm
x = 128.571 °
y = 51.4286 °
Agenda:
r = inradius (apothem)
R = circumradius
a = side length
n = number of sides
x = interior angle
y = exterior angle
A = area
P = perimeter
π = pi = 3.14159...
√ = square root
Formula: A = (1/4)na2 cot(π/n) = nr2 tan(π/n)
Answer:
The correct option is: B. 2,125 squared cm.
Step-by-step explanation:
Formula for the Area of a regular polygon is......
[tex]A= \frac{1}{2}r^2 n\ sin(\frac{360}{n})[/tex]
where, [tex]r=[/tex] radius, [tex]n=[/tex] number of sides.
Here the polygon is a regular heptagon with radius of 27.87 cm.
That means, [tex]n=7,\ \ r= 27.87\ cm[/tex]
Plugging these values into the above formula........
[tex]A=\frac{1}{2}(27.87)^2(7)\ sin(\frac{360}{7})\\ \\ A=\frac{1}{2}(776.7369)(7)(0.7818)\\ \\ A=2125.4707... \approx 2125\ (rounded\ to\ nearest\ whole\ number)[/tex]
So, the approximate area of the heptagon will be 2125 squared cm.