The area of a polygon is given by the formula Area = ap/2 where a is the length of the apothem and p is the perimeter. The apothem is a line from the center of the polygon perpendicular to a side.
Depending on the formula you know, you can find the length of a side in 1 of 2 ways.
The first way uses a triangle. Using the radius of the polygon you can create 8 congruent triangles. The center angle will be 360 / 8 = 45 and two side lengths of 20. You can find the length of the base using the law of cosines.
c^2 = 20^2 + 20^2 - 2(20)(20)(cos 45)
c^2 = 400 + 400 - 800(cos 45)
c^2 = 800 - 800(cos 45)
c = sqrt(800 - 800(cos 45)
c = 15.31
The second way is to use this formula:
r = s / (2 sin(180 / n))
20 = s / (2 sin(180/8)
(20)(2)sin(22.5) = s
(40)sin(22.5) = s
s = 15.31
We need to calculate the perimeter. As there are 8 sides (8)(15.31) = 122.48
Now we need to calculate the apothem using
a = S / (2 tan (180 / n)
a = 15.31 / (2 tan (180 / 8))
a = 18.48
Now solve for the area
Area = ap/2
Area = (18.48)(122.48)/2
Area = 1131.72
perimeter = 122.48
area = 1131.72
Answer:
100
Step-by-step explanation:
4 spirals for 1 student. 4 x 25 to get the total number, and that equals 100
Answer:
y = - 1/2x + 1
Step-by-step explanation:
y+2= - 1/2x
Slope = -1/2
Point: (-2,2)
y-Intercept: 2 - (-1/2)(-2) = 2 - 1 = 1
Answer:
3,4,5 are congruent angles
Step-by-step explanation:
Congruent Angles have the same angle (in degrees or radians). That is all. They don't have to point in the same direction. They don't have to be on similar sized lines.
Answer:Number of small boxes shipped = 8
Number of large boxes shipped = 13
Step-by-step explanation:
Step-by-step explanation:
Let x be the number of small boxes and let y be the number of large boxes
According to the first statement, a total of 21 boxes were shipped
Equation 1 will be:
x+y=21
According to 2nd statement, the total weight was 1110 and we know the weight of one small box is 25 and large box is 70
Equation 2 will be:
25x+70y=1110
Use the substitution method for solving the equation
Putting the value of x in equation 2
25(21-y) +70y =1110
525-25y+70y = 1110
45y = 585
Y=13
Putting the value of y in equation 1
x+13 = 21
X = 8
Number of small boxes shipped = 8
Number of large boxes shipped = 13
