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alexandr1967 [171]
3 years ago
13

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.
Mathematics
2 answers:
Nady [450]3 years ago
6 0

Answer:

<em>The correct option is:  B.  2,125 squared cm.</em>

Step-by-step explanation:

<u>Formula for the Area of a regular polygon</u> is......

A= \frac{1}{2}r^2 n\ sin(\frac{360}{n})

where,  r= radius, n= number of sides.

Here the polygon is a regular <u>heptagon</u> with <u>radius of 27.87 cm</u>.

That means, n=7,\ \ r= 27.87\ cm

Plugging these values into the above formula........

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)

So, the approximate area of the heptagon will be 2125 squared cm.

Andre45 [30]3 years ago
3 0
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...
<span>√ = square root
</span>
Formula: A = (1/4)na2 cot(π/n) = nr2 tan(π/n)
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