Math Is Fun Forum

zee-f

Member

Registered: 2011-05-12

Posts: 1,220

Area and Volume of Prisms and Pyramids

Hi,

I  got the following incorrect I really need help

For 1 through 10,#5 what is the area and volume of the given shape, if the length of one side of the base is 6, the height is 8, and the slant height is 10?

5.C
5. the base is an isosceles triangle with a height of  8 and a base of 3 (sides of 6)

A Lateral area: 120; Volume: 18*sqrt(15)
BLateral area: 100; Volume: 96
CLateral area: 192; Volume: 144
DLateral area: 176; Volume: 18*sqrt(15)
E Lateral area: 288; Volume: 288
F Lateral area: 240; Volume: 64

I have an isosceles triangle with a height of 4 and a base of 6:
11- C (this was correct)
11. What is the area?
A 19
B 35
C 12
D 16
E 22
F 54

This triangle just became the base of a regular prism, with a height of 8:
12-F
12. What is the lateral area?

A 105
B 28
C 35
D 128
E 56
F 12

13-C
13. What is the area of the largest rectangular side?
A 95
B 54
C 32
D 48
E 96
F 10

Last edited by zee-f (2012-11-27 06:28:16)

---

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Area and Volume of Prisms and Pyramids

hi zee-f

If you got the rest correct, that was very good, well done.

Now for the corrections:

5.C
5. the base is an isosceles triangle with a height of  8 and a base of 3 (sides of 6)

A Lateral area: 120; Volume: 18*sqrt(15)
BLateral area: 100; Volume: 96
CLateral area: 192; Volume: 144
DLateral area: 176; Volume: 18*sqrt(15)
E Lateral area: 288; Volume: 288
F Lateral area: 240; Volume: 64

I'm thinking this is a prism, that is 8 tall.  It has an isosceles trianle for a base, with sides 6, 6 and 3.

So the perimeter is 6 + 6 + 3 = ?

So the lateral area = perimeter x 8.

Now for the volume.

You have to work out the height of the triangle.

I'll use Pythagoras to get it.

Split the triangle in half so that there's a right angle.  Hypotenuse = 6  shortest side = 1.5

Then multiply by 8

I got a decimal answer for this, so I had to check what 18 x sqrt(15) comes to.

I have an isosceles triangle with a height of 4 and a base of 6:
11- C (this was correct)
11. What is the area?
A 19
B 35
C 12
D 16
E 22
F 54

This triangle just became the base of a regular prism, with a height of 8:
12-F
12. What is the lateral area?

A 105
B 28
C 35
D 128
E 56
F 12

You need to work out the sides.  The base is 6 but what about the two equal sides.

If you split the isosceles triangle down the middle to make a right angle.  Half the base is 3  and the height is 4.

Then perimeter is this answer twice plus the base.  Then multiply by 8.  I can see the answer in the list.

13-C
13. What is the area of the largest rectangular side?
A 95
B 54
C 32
D 48
E 96
F 10

And you can get the largest by taking the longest side and multiplying by 8.

I can see this answer in the list.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

zee-f

Member

Registered: 2011-05-12

Posts: 1,220

Re: Area and Volume of Prisms and Pyramids

ok So number #5-

p=15
LA= 15*8=120

V=BH
But when I used the  Pythagoras theorem I got

a²+b²=c²
1.5²+b²=6²

2.25+b²=36

b²= 15/4

b= 3√15 / 2

---

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Area and Volume of Prisms and Pyramids

hi zee-f

120 is correct for the area.

b= 3√15 / 2 is also correct for the height of the triangle.

Now you can do half base x height to get the area of the triangle and then multiply by the length of the prism.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

zee-f

Member

Registered: 2011-05-12

Posts: 1,220

Re: Area and Volume of Prisms and Pyramids

So now I have to get the area of the base and multiply it by the height of the prism to get the volume right?

half base = 3
height =  3√15 / 2
So 1/2 * 3  *  3√15 / 2 = 9√15/4

9√15/4 * 8 = 18√15

---

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

zee-f

Member

Registered: 2011-05-12

Posts: 1,220

Re: Area and Volume of Prisms and Pyramids

#12-
4²+3²=c²
16+9=25
√25=5

5*2+6=16
16*8=128

So #12- D

#13- Longest side is 6 So 6*8= 48

So I got the 8 by multiplying 4 *2 right?

---

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Area and Volume of Prisms and Pyramids

Q5 all correct.

Q12 Correct

Q13 Correct. 

So I got the 8 by multiplying 4 *2 right?

No.  It is the height of the prism.

This triangle just became the base of a regular prism, with a height of 8:

Well done for all correct !! 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

zee-f

Member

Registered: 2011-05-12

Posts: 1,220

Re: Area and Volume of Prisms and Pyramids

Thank you!! )

---

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3