the solid is made up of 2 regular octagons, 8 sides, joined up by 8 rectangles, one on each side towards the other octagonal face.
from the figure, we can see that the apothem is 5 for the octagons, and since each side is 3 cm long, the perimeter of one octagon is 3*8 = 24.
the standing up sides are simply rectangles of 8x3.
if we can just get the area of all those ten figures, and sum them up, that'd be the area of the solid.
![\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=5\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(5)(24)\implies \stackrel{\textit{just for one octagon}}{A=60} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{two octagon's area}}{2(60)}~~+~~\stackrel{\textit{eight rectangle's area}}{8(3\cdot 8)}\implies 120+192\implies 312](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20regular%20polygon%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B2%7Dap~~%20%5Cbegin%7Bcases%7D%20a%3Dapothem%5C%5C%20p%3Dperimeter%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a%3D5%5C%5C%20p%3D24%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B2%7D%285%29%2824%29%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bjust%20for%20one%20octagon%7D%7D%7BA%3D60%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Btwo%20octagon%27s%20area%7D%7D%7B2%2860%29%7D~~%2B~~%5Cstackrel%7B%5Ctextit%7Beight%20rectangle%27s%20area%7D%7D%7B8%283%5Ccdot%208%29%7D%5Cimplies%20120%2B192%5Cimplies%20312)
This will only have one solution because it does not deal with a quadratic. Then to isolate x you need to get the similar terms on different sides by subtracting or adding, Then divide both sides by the number next to x (coefficient).
T us assume the two numbers to be "x" and "y".
Then
2x + y = 310
And
x - y = 55
Let us take the second equation and find the value of x in relation to y.
x - y = 55
x = y + 55
Now let us put the value of x in the first equation, we get
2x + y = 310
2(y + 55) + y = 310
2y + 110 + y = 310
3y = 310 - 110
3y = 200
y = 200/3
= 66 2/3
Now putting the value of y in the second equation, we get
x - y = 55
x - (200/3) = 55
3x - 200 = 55 * 3
3x = 165 + 200
x = 365/3
= 121 2/3
So the value of x is 121 2/3 and the value of y is 66 2/3
Its same i think
100-40=60
130-70=60
Answer:320
Step-by-step explanation:
2/5 of the students surveyed lisen to country. So to make the percentage fit the total student population, you figure out what your 2/5 is in a percetnage. That comes out to 40%. so, 40% of 800 is 320.
