# Square prism

#### Stefany

##### New member
How do I find the surface area of a square prism if I don’t know it’s height?
The only thing I know is a and v...

#### JeffM

##### Elite Member
What do a and v represent?

#### Stefany

##### New member
What do a and v represent?
a=8
V=448
With them I found B, which is 64, but I don’t think that will help me with the surface area.

#### JeffM

##### Elite Member
You have told me what the values are. What do they represent? For example, is v volume?

#### Stefany

##### New member
You have told me what the values are. What do they represent? For example, is v volume?
a is the side of the square; V is the volume; B is the base area.

#### JeffM

##### Elite Member
$$\displaystyle v = a^2h$$, correct, where h is height?

So, given v and a, can you find h?

What is the formula for the surface area?

#### Stefany

##### New member
$$\displaystyle v = a^2h$$, correct, where h is height?

So, given v and a, can you find h?

What is the formula for the surface area?
Yes, I’ll be able to find h with that formula but I also found another one which is V=B.h

The formula I have for s is S=P.h
I’ll be able to find P then once I have the height I’ll just multiply them.

Thanks for the formula

#### Jomo

##### Elite Member
s and S are different variables, so please use just one of them if they are equal. Now please tell us what P and s represents!

#### Stefany

##### New member
s and S are different variables, so please use just one of them if they are equal. Now please tell us what P and s represents!
S is the surface area and P is the perimeter of the square.

#### firemath

##### Full Member
How do I find the surface area of a square prism if I don’t know it’s height?
The only thing I know is a and v...
This is a rectangular prism, not a square prism.
S is the surface area and P is the perimeter of the square.
The perimeter of the base (it's not a square anyway, it's a rectangle).
a is the side of the square; V is the volume; B is the base area.
The side of the base, you mean? This is becoming confusing for no reason. Please use the correct terms, and we'll all be much less bewildered.

#### Dr.Peterson

##### Elite Member
This is a rectangular prism, not a square prism.

The perimeter of the base (it's not a square anyway, it's a rectangle).

The side of the base, you mean? This is becoming confusing for no reason. Please use the correct terms, and we'll all be much less bewildered.
What am I missing? The OP said it's a square prism!
How do I find the surface area of a square prism if I don’t know it’s height?
The only thing I know is a and v...
Yes, I’ll be able to find h with that formula but I also found another one which is V=B.h

The formula I have for s is S=P.h
I’ll be able to find P then once I have the height I’ll just multiply them.

Thanks for the formula
V=Bh applies to any prism at all, including your square prism; B = a^2.

But S=Ph gives only the lateral surface area (for any prism). You need to add on the area of the bases. What is P for a square with side a?

#### firemath

##### Full Member
What am I missing? The OP said it's a square prism!

V=Bh applies to any prism at all, including your square prism; B = a^2.

But S=Ph gives only the lateral surface area (for any prism). You need to add on the area of the bases. What is P for a square with side a?
If we call it a rectangular prism (squares are rectangles) we'll be able to assign our variables more clearly. L, W, etc.

Technically the height is (don't click on this, OP, until you've solved it) -> 7, so doesn't that make it a rectangular prism as well?

But whatever. You know way more than me.

#### Stefany

##### New member

This is a rectangular prism, not a square prism.

The perimeter of the base (it's not a square anyway, it's a rectangle).

The side of the base, you mean? This is becoming confusing for no reason. Please use the correct terms, and we'll all be much less bewildered.
Sorry for making it confusing...
I said it was a square prism because all of the sides are equal.

Anyways, I figured it out and solved it.

#### Stefany

##### New member
What am I missing? The OP said it's a square prism!

V=Bh applies to any prism at all, including your square prism; B = a^2.

But S=Ph gives only the lateral surface area (for any prism). You need to add on the area of the bases. What is P for a square with side a?
Since a is 8 then P is 32.
Thanks for your help, but like I mentioned earlier I was able to solve it

#### firemath

##### Full Member

Sorry for making it confusing...
I said it was a square prism because all of the sides are equal.

Anyways, I figured it out and solved it.
No problem. I'm just nitpicking.... .

#### Dr.Peterson

##### Elite Member
If we call it a rectangular prism (squares are rectangles) we'll be able to assign our variables more clearly. L, W, etc.

Technically the height is (don't click on this, OP, until you've solved it) -> 7, so doesn't that make it a rectangular prism as well?
Yes, if it's a square, it's also a rectangle, and formulas for rectangles apply. But you said it wasn't a square! And the OP (previously) gave the formula for volume of a square prism, which does apply (and which uses the variable a).

You said, "This is a rectangular prism, not a square prism."

I suspect, now, that what you intended to say was, "This is the formula for a rectangular prism, not specifically for a square prism." But that isn't what you said. I can only respond to what you say, not to what you might have been thinking ...