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hellp! -find the perimeter and area of the regular polygon
- Thread starter marwee
- Start date
Use the formulas:
\(\displaystyle \L \;P\,=\,ns\)
\(\displaystyle P\,=\,perimeter\,,\,n\,=\,#\,of\,sides\,,\,s\,=\,side\,\,length\)
\(\displaystyle \L \;A\,=\,0.5ans\,\to\,0.5aP\)
\(\displaystyle A\,=\,area\,,\,a\,=\,apothem\,,\,n\,=\,#\,of\,sides\,,\,s\,=\,side\,length\,,\,P\,=\,perimeter\)
Try something neat with these formulas.
\(\displaystyle \L \;P\,=\,ns\)
\(\displaystyle P\,=\,perimeter\,,\,n\,=\,#\,of\,sides\,,\,s\,=\,side\,\,length\)
\(\displaystyle \L \;A\,=\,0.5ans\,\to\,0.5aP\)
\(\displaystyle A\,=\,area\,,\,a\,=\,apothem\,,\,n\,=\,#\,of\,sides\,,\,s\,=\,side\,length\,,\,P\,=\,perimeter\)
Try something neat with these formulas.
Regular Polygon Terminology
n = the number of sides
v = angle subtended at the center by one side = 360/n
s = the length of one side = R[2sin(v/2)] = r[2tan(v/2)]
R = the radius of the circumscribed circle = s[csc(v/2]/2 = r[sec(v/2)]
r = the radius of the inscribed circle = R[cos(v/2)] = s[cot(v/2)]/2
a = apothem = the perpendicular distance from the center to a side (the radius of the inscribed circle)
p = the perimeter = ns
Area = s^2[ncot(v/2)]/4 = R^2[nsin(v)]/2 = r^2[ntan(v/2)]
The formula for the area of a regular polygon is also A = (1/2 )ap = (1/2)ans, where a is the apothem, p is the perimeter, s is the side length and n is the number of sides..
The sum of all the interior angles in a polygon is 180(n - 2)
The sum of the exterior angles in a polygon is 360º.
The internal angle between two adjacent sides of a regular polygon is given by 180(n - 2)/n
The external angle between any side and the extended adjacent side of a regular polygon is given by 360/n.
You might be interested in why the sum of all the interior angles of a polygon is 180(n - 2).
Consider first the square, rectangle and trapazoid. Draw one ofthe diagonals in each of these figures.
What is created is two triangles within each figure.
The sum of the interior angles of any triangle is 180 deg.
Therefore, the sum of the interior angles of each of these 4 sided figues is 360 Deg.
Now consider a pentagon with 5 sides that can be divided up into 3 triangles.
Therefore, the sum of the interior angles of a pentagon is 540 Deg.
What about a hexagon. I tink you will soonsee that the sum of the interior angles is 720 Deg.
Do you notice anything?
n = number of sides........3........4........5........6
Sum of Int. Angles.........180....360....540....720
The sum of the interior angles is representable by 180(n - 2).
Consider also the sum of the exterior angles.
Each exterior angle is 180 - 180(n - 2)/n = (180 - 180n + 360)/n = 360/n.
Therefore, the sum of the exterior angles is 360n/n or 360 Deg.
n = the number of sides
v = angle subtended at the center by one side = 360/n
s = the length of one side = R[2sin(v/2)] = r[2tan(v/2)]
R = the radius of the circumscribed circle = s[csc(v/2]/2 = r[sec(v/2)]
r = the radius of the inscribed circle = R[cos(v/2)] = s[cot(v/2)]/2
a = apothem = the perpendicular distance from the center to a side (the radius of the inscribed circle)
p = the perimeter = ns
Area = s^2[ncot(v/2)]/4 = R^2[nsin(v)]/2 = r^2[ntan(v/2)]
The formula for the area of a regular polygon is also A = (1/2 )ap = (1/2)ans, where a is the apothem, p is the perimeter, s is the side length and n is the number of sides..
The sum of all the interior angles in a polygon is 180(n - 2)
The sum of the exterior angles in a polygon is 360º.
The internal angle between two adjacent sides of a regular polygon is given by 180(n - 2)/n
The external angle between any side and the extended adjacent side of a regular polygon is given by 360/n.
You might be interested in why the sum of all the interior angles of a polygon is 180(n - 2).
Consider first the square, rectangle and trapazoid. Draw one ofthe diagonals in each of these figures.
What is created is two triangles within each figure.
The sum of the interior angles of any triangle is 180 deg.
Therefore, the sum of the interior angles of each of these 4 sided figues is 360 Deg.
Now consider a pentagon with 5 sides that can be divided up into 3 triangles.
Therefore, the sum of the interior angles of a pentagon is 540 Deg.
What about a hexagon. I tink you will soonsee that the sum of the interior angles is 720 Deg.
Do you notice anything?
n = number of sides........3........4........5........6
Sum of Int. Angles.........180....360....540....720
The sum of the interior angles is representable by 180(n - 2).
Consider also the sum of the exterior angles.
Each exterior angle is 180 - 180(n - 2)/n = (180 - 180n + 360)/n = 360/n.
Therefore, the sum of the exterior angles is 360n/n or 360 Deg.