Answer:
The area of a regular octagon with a perimeter of 80 ft and an apothem of 12.07 feet is 482.8 ft².
Step-by-step explanation:
An octagon is a polygon with eight sides. An octagon is regular (also called a regular octagon) is a polygon with all eight sides equal.
The apothem of a regular octagon is the shortest distance between the center and any of its sides, in other words, it is the distance that separates the center of the polygon from the central point of each side of the octagon.
The area is calculated using the following formula:
Where:
- n is the number of sides.
- L is the length of one of the sides.
- Ap is the value of the apothem.
Being n = 8 being an octagon and the perimeter P the sum of the sides of the octagon (P = 8 * L), the area of the regular octagon can be calculated by:
In this case:
Replacing:
Solving:
Area=482.8 ft²
<u><em>The area of a regular octagon with a perimeter of 80 ft and an apothem of 12.07 feet is 482.8 ft².</em></u>
Rate of change between 1 and 3: find the y values for 1 and 3:
Rate of change = (6-1) / (3-1) = 5/2
Rate of change from 2 and 4:
= (10-3) / (4-2) = 7/2
The rate from 2 to 4 is larger because 7/2 is larger than 5/2
Answer:
-2x-14
Step-by-step explanation:
Answer:
The largest possible volume V is ;
V = l^2 × h
V = 20^2 × 10 = 4000cm^3
Step-by-step explanation:
Given
Volume of a box = length × breadth × height= l×b×h
In this case the box have a square base. i.e l=b
Volume V = l^2 × h
The surface area of a square box
S = 2(lb+lh+bh)
S = 2(l^2 + lh + lh) since l=b
S = 2(l^2 + 2lh)
Given that the box is open top.
S = l^2 + 4lh
And Surface Area of the box is 1200cm^2
1200 = l^2 + 4lh ....1
Making h the subject of formula
h = (1200 - l^2)/4l .....2
Volume is given as
V = l^2 × h
V = l^2 ×(1200 - l^2)/4l
V = (1200l - l^3)/4
the maximum point is at dV/dl = 0
dV/dl = (1200 - 3l^2)/4
dV/dl = (1200 - 3l^2)/4 = 0
3l^2= 1200
l^2 = 1200/3 = 400
l = √400
I = 20cm
Since,
h = (1200 - l^2)/4l
h = (1200 - 20^2)/4×20
h = (800)/80
h = 10cm
The largest possible volume V is ;
V = l^2 × h
V = 20^2 × 10 = 4000cm^3
