Answer:
Federcio's age possible values are those that are greater than 14 i.e 15, 16, 17 and so on
Step-by-step explanation:
Let Federico's age = x
Three times the difference of Federico’s age, and 4 means:
3(x - 4)
Increased by 7:
3(x - 4) + 7
Is greater than 37:
3(x - 4) + 7 > 37
Solving the inequality:
3x - 12 + 7 > 37
3x - 5 > 37
3x > 37 + 5
3x > 42
x >42/3
x > 14
Federcio's age possible values are those that are greater than 14
The area of the regular octagon is calculated as half of the product of the perimeter and the apothem (ap), using the formula of the area of the regular polygon.
We have then:
A = ((p) * (ap)) / 2
Where,
p: perimeter
ap: apotema
Substituting values:
A = ((8 * 3.4) * (4.2)) / 2
A = 57.12 in ^ 2
Answer:
the area of the regular octagon is:
B. 57
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
