Find the area of the regular polygon. Round your answer to the nearest tenth.
the individual sides are 10 the radius is 13.07
If your radius is to the corners, then
10 = 2* 13.07 sin (180/n)
sin (180/n) = .382555
180/n = 22.5
n = 8 sides
360/8 = 45 = top angle of each isoceles triangle
half of that has hpotenuse of 13.07 and base of 5
area of each of those 16 triangles = (1/2) (5)(13.07 cos 22.5) = 30.2
16*30.2 = 483
radius to what where with center where?
the 10 is on one of the lines of the polygon then a line from the center
goes from the center to the edge of polygon inside with a doted line
does that help
please help me with this
thank you
Trigonometry and Area Practice
1.) D, 173.8
2.) A, 7,554
3.) A, 311.3
4.) C, The area of pentagon A is equal to 1.53 times the area of pentagon B.
5.) D, 48.2
6.) C, 237.8
7.) C, 20.8
8.) A, 29.7
9.) D, $51.96
10.) C, 24in
amosc :) - annee-mrie
To find the area of a regular polygon, you can use the formula:
Area = (1/2) × (A × P)
Where:
A is the apothem of the polygon (distance from the center to any side)
P is the perimeter of the polygon (the total length of all sides)
In this case, you are given the length of the sides, which is 10. Therefore, the perimeter (P) can be calculated by multiplying the length of a side by the number of sides in the polygon.
Since the polygon is regular, the apothem and the radius are the same. Therefore, the apothem (A) is given as 13.07.
Let's now calculate the perimeter of the polygon (P):
P = 10 × (number of sides)
To determine the number of sides of the polygon, we can use the formula:
n = 360 / (180 - interior angle)
For a regular polygon, all interior angles are equal. So, we need to find the measure of one interior angle.
In a regular polygon, each interior angle can be calculated using the formula:
Interior angle = (n - 2) × 180 / n
where n is the number of sides.
Now, we can calculate the number of sides and the interior angle:
n = 360 / (180 - interior angle)
Next, we substitute the length of a side (10) into the perimeter formula:
P = 10 × (number of sides)
Having calculated the perimeter (P) and the apothem (A), we can now find the area of the regular polygon using the formula:
Area = (1/2) × (A × P)
Remember to round your answer to the nearest tenth as specified.
If your radius is to the center of each side then
tan (360/2n) = 5/13.07
180/n = 20.93
n = 8.59 sides
I doubt if that is what it means so use my previous answer.