Main content

### Course: Geometry (all content) > Unit 8

Lesson 3: Surface area- Intro to nets of polyhedra
- Nets of polyhedra
- Surface area using a net: triangular prism
- Surface area of a box (cuboid)
- Surface area of a box using nets
- Surface area using nets
- Surface area
- Surface area using a net: rectangular prism
- Volume and surface area word problems
- Surface area review

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Surface area review

Review surface area and try some practice problems.

## What is surface area?

**Surface area**is the amount of space covering the outside of a three-dimensional shape.

## Finding surface area

To calculate surface area, we add the areas of all the faces of the three-dimensional figure.

*Want to learn more about finding surface area? Check out this video.*

### Example: Rectangular prism

**Find the surface area of the right rectangular prism shown below.**

Let's draw a net of the rectangular prism.

Each of the sides is a $4$ by $1.5$ rectangle.

The total area of both sides is $2\cdot 6={12}$ .

The bottom and the top are both $4$ by $5$ rectangles.

The total area of bottom and the top is $2\cdot 20={40}$ .

The back and the front are both $1.5$ by $5$ rectangles.

The total area of the back and the front is $2\cdot 7.5={15}$ .

Let's add the areas to find the surface area.

**The surface area of the rectangular prism is**$67$ units${}^{2}$ .

## Want to join the conversation?

- How do you find the surface area of a cylinder??(109 votes)
- Actually if the radius is r, the surface area is 4*pi*r^2(61 votes)

- Would it be possible to find the surface area of a sphere?(40 votes)
- if the radius is r, the surface area is 4*pi*r^2(24 votes)

- the question to find the surface area of a square with sides 2 1/2 confuses me. can someone please explain in detail how to solve this problem?(20 votes)
- Basically, 2 1/2 equals 2.5. So the easiest way to do that is obviously by multiplying 2.5*2.5*6 By the way, * equals multiply.(22 votes)

- What if we don't have a decimal and just a normal number?(12 votes)
- That's ok, you won't always get a decimal or fraction.

Hope this helps, have a great day.(24 votes)

- How do you find the surface area of a cylinder(15 votes)
- The total surface area of the cylinder formula is the sum of the base surface area and the lateral surface area: total_area = base_area + lateral_area , or total_area = 2 * π * r² + (2 * π * r) * h , or total_area = 2 * π * r * (r + h) .(10 votes)

- how to find the area of a square pyramid?(10 votes)
- I assume you mean the surface area, since a square pyramid is 3-dimensional.

For a right square pyramid with base side length s and slant height L, the total surface area is the area of the square base with side length s, plus the total area of four triangles each with base s and altitude L. So the total surface area is

s^2 + 4(1/2)(sL) = s^2 + 2sL.

(Note well: the slant height is**not**the same as the vertical height.)(14 votes)

- I Get it but I still need help and a little bit of practice(17 votes)
- i don't get it either(0 votes)

- How do you find the height of a cuboid, when the length, the width and the surface area is given?(11 votes)
- Surface area of cuboid = 2(lb+bh+hl)

So you put the values and then solve.(9 votes)

- How about to find the surface area of a hyperboloid?(13 votes)
- Why are questions called quetions... The more you know.........The less you are(13 votes)
- why is this so funny to me? anybody else??(2 votes)