Answer:
600 ft³
Step-by-step explanation:
Base area: B
Base is triangle
base = 12 ft and height = 5 ft
Area of triangle = B = 
H = 20 ft
Volume = B * H
= 30 * 20
= 600 ft³
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:
1). 0.625
2). 0.5
3). 0.6
4). 1.75
5). 0.6666 (repeating decimal)
hope this helped!
we are given
We will simplify left side and make it equal to right side
Left side:
we can use trigonometric identity
we can replace it
we know that
csc=1/sin and sec=1/cos
so, we can replace it
and we get
now, we know that
tan =sin/cos
we can simplify it
and we get
we can also write it as
Right Side:
we can see that
left side = right side
so,
......Answer
