1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sveta [45]
3 years ago
10

WILL GIVE BRAINLIEST FIND VOLUME 60 is the area of the base

Mathematics
1 answer:
scoundrel [369]3 years ago
4 0
Hey so yeah this can be a challenging problem, Vol (V) is much easier to solve than surface area (SA), but I'll show you how it's done, my friend.
First of all, V (prism) = area of base (B) × h
We know that the height (h) of this prism is given, which we'll need later on: h = 5 ft, and area of base (B) is given as 60 ft2
So V = 60 ft2 × 5 ft = 300 ft3

So now for the hard part... how to calculate the SA of this prism

IF YOU DON'T NEED SA FOR THIS TYPE OF PROBLEM, DO NOT PROCEED!!!
[VERY DETAILED]

means solving the dimensions (sides) of that pesky polygon base (B) or lid.
The most important things about polygons are:
1) is it regular (same angle ° and side length)??
2) How many sides or angles??

This has to be regular, because they give you no other info so it has to be, in order to solve. And then it has 5 sides and angles = regular pentagon. ("penta" means 5).

Now there are 360° in any circle, so:
take the central angles of where the sides meet at the center forming triangles (see drawing above), each of those (5) central <'s = 360/5 = 72°
Now the apex of each of these triangles = 72°
but with our 5 triangles, we need to find the height of each triangle -- which is the midpoint of the side (base (b) of triangle), and h is perpendicular to this b. By bisecting that apex angle of 72, it forms 2 equal right triangles of
72/2 = 36°. So each right triangle has 36, 90, and?? 180-36-90 = 90-36 = 54°
let's call the base (b) = 1 side of pentagon
= side (s)
Therefore (see 2nd image drawn above) tangent (tan) of € = opposite/adjacent, or
tan (54) = h÷1/2b --> h = [tan (54)]×(1/2)b
1/2b = h/[tan (54)] = h/1.38

Also the area of each of the larger 5 triangles A(t) = 1/2b×h, and that area A(t) × 5 = area of whole pentagon base A(B)
So now after all that... our A(B) given at beginning = 60ft2. let's put it all together:
1/2b = h/[tan (54)] = h/1.38
A(t) = 1/2b×h, and A(B) = 5×A(t)
which means that A(B) = 5×(1/2b×h)
AND since the other calculation shows that 1/2b = h/1.38, plug that value into the A(B) formula...
.
.
.

now that we have height (h) of each triangle, we can go back to our tan equation for the triangle: tan (54) = 1.38 = h/(1/2b)
--> 1/2×b = h/1.38 --> base (b) = 2h/1.38
b = 2(4.06 ft)/1.38 = 8.12 ft/1.38 = 5.90 ft, for which b us also the width of each rectangular side panel (w)
length (l) of these sides was given as height of the whole prism = 5 ft

NOW FINALLY... THE FINAL SURFACE AREA OF THE PRISM (SA) = (2×A(B)) + (5×rectangular side)
SA = (2×60 ft​2) + (5×(l×w)) = 120 ft2 + 5×5ft×5.9ft
SA = 120 ft2 + 147.62 ft2 = 267.62 ft2

You might be interested in
Find the point-slope equation for the line that passes through the points (5,19) and (-5,-1).
xxTIMURxx [149]

Answer: y - 19 = 2(x - 5)

Step-by-step explanation:

The point slope form is expressed as

y - y1 = m(x - x1)

Where

m represents slope

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The given points are (5,19) and (-5,-1)

y2 = - 1

y1 = 19

x2 = - 5

x1 = 5

Slope,m = (- 1 - 19)/(- 5 - 5) = - 20/- 10 = 2

To determine the equation, we would substitute x1 = 5, y1 = 19 and m= 2 into the point slope form equation. It becomes

y - 19 = 2(x - 5)

7 0
3 years ago
Read 2 more answers
Carina says that to divide by 12, she will need to write 12 as the fraction and then divide. Is she correct? Explain your reason
Alika [10]

Answer:

I do not know

Step-by-step explanation:

I think so

6 0
2 years ago
I need help with this question please.
Reil [10]

Answer:

10 n equals 6

Step-by-step explanation:

Why? Because that has nothing to do with the problem and no solution for 3/5.

7 0
2 years ago
The vertices of figure EFGH have coordinates E(1, 3), F(2, 5), G(4, 4) , and H(3, 3) . The vertices of figure E'F'G'H' have coor
ad-work [718]
The correct answer is A) a translation 2 units right and 4 units down.

Both of the reflections listed would keep the digits but change their signs and/or placement.
A translation 2 units right subtracts 2 from the x-coordinate.  A translation 4 units down subtracts 4 from the y-coordinate.  Comparing each pre-image point to its image, we can see that is what happened.
7 0
3 years ago
A(n) ______ shows a corner view of a three-dimensional figure.
Mashutka [201]

Answer:

Isometric Drawing

8 0
3 years ago
Read 2 more answers
Other questions:
  • An airplane is flying from New York city to Los Angeles.The distance it travels in Miles, D, is related to the time in seconds,
    9·1 answer
  • Help plz 30 pts who solve
    9·1 answer
  • Find the sum of 142.3, 0.572 and 47.06​
    12·2 answers
  • Which best describes the relationship between the successive terms in the sequence below?
    14·2 answers
  • Which of the following equations correctly represents a property of image?
    14·1 answer
  • Which equation represents a proportional relationship?
    12·1 answer
  • Someone please help
    5·1 answer
  • I need help i will give the brainliest!
    8·1 answer
  • PRECALC, please help
    8·1 answer
  • I need help with 3 problems.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!