MATH SOLVE

4 months ago

Q:
# a regular heptagon has a radius of approximately 27.87cm and the lengthof each side is 24.18cm. what is the approximate area of the heptagon rounded to the nearest whole number? recall that a polygon with 7 sides. A. 1,173 squared cm. B. 2,125 squared cm. C. 2,359 squared cm. D. 4,250 squared cm.

Accepted Solution

A:

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)