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)
Answer:
B
Step-by-step explanation:
Just read and you will see why i say that
Full question:
Heng was trying to factor 10x²+5x. She found that the greatest common factor of these terms was 5x and made an area model: What is the width of Heng's area model?
Answer:
The width of the area model is 2x + 1
Step-by-step explanation:
Given
Expression: 10x² + 5x
Factor: 5x
Required
Width of the Area Model
To solve this, I'll assume the area model is Length * Width
Provided that we're to solve for the width of the model.
This implies that; Length = 5x
Area = Length * Width
And
Area = 10x² + 5x
Equate these two
Length * Width = 10x² + 5x
Factorize express on the right hand side
Length * Width = 5x(2x + 1)
Substitute 5x for Length
5x * Width = 5x(2x + 1)
Divide both sides by 5x
Width = 2x + 1
Hence, the width of the area model is 2x + 1
90= 3x + 2x
90= 5x
x= 18
one measure = 3(18)= 54
the other one= 2(18)= 36
hope this helps!
Answer:
A
Step-by-step explanation:
A cube has 6 sides
Only one side of the cube has 2 on it
The probability of getting 2 would be 1/6
Only one side of the cube has 6 on it
The probability of getting 6 would be 1/6
For both events to happen together
1/6 x 1/6 = 1/36
