If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: 6th grade (Illustrative Mathematics)>Unit 1

Lesson 10: Lesson 15: More nets, more surface area

# 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.
$\begin{array}{rl}\text{Area of a rectangle}& =\text{length}\cdot \text{width}\\ \\ & =4\cdot 1.5\\ \\ & =6\\ \end{array}$
The total area of both sides is $2\cdot 6=12$.
The bottom and the top are both $4$ by $5$ rectangles.
$\begin{array}{rl}\text{Area of a rectangle}& =\text{length}\cdot \text{width}\\ \\ & =4\cdot 5\\ \\ & =20\\ \end{array}$
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.
$\begin{array}{rl}\text{Area of a rectangle}& =\text{length}\cdot \text{width}\\ \\ & =1.5\cdot 5\\ \\ & =7.5\\ \end{array}$
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.
$\begin{array}{rl}\text{Surface area}& =12+40+15\\ \\ & =67\\ \end{array}$
The surface area of the rectangular prism is $67$ units${}^{2}$.

## Practice set

Problem 1
Find the surface area of the square pyramid shown below.
units${}^{2}$

Want to try some more surface area problems? Check out this exercise.

## Want to join the conversation?

• How do you find the surface area of a cylinder??
• Actually if the radius is r, the surface area is 4*pi*r^2
• Would it be possible to find the surface area of a sphere?
• if the radius is r, the surface area is 4*pi*r^2
• 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?
• 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.
• What if we don't have a decimal and just a normal number?
• That's ok, you won't always get a decimal or fraction.

Hope this helps, have a great day.
• How do you find the surface area of a cylinder
• 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) .
• I Get it but I still need help and a little bit of practice
• i don't get it either
• how to find the area of a square pyramid?
• 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.)