moomoomath logo header
lime green horizontal line
Welcome to MooMooMath
Quick Math Homework Help
study skills A teachers secret guide to your best grades
Master the 7 pillars of school success that I have learned from 25 years of teaching.

Improve your grades and lower your stress
A-Z Video List
diagonals of a square
area of square formula header
area of square formula headerarea of square formula headerarea of square formula header
area of square formula header
area of square formula header
area of square formula headerarea of square formula headerarea of square formula header
area of square formula header
Example 1 Find the area of a square with a side of 8 units. 







Step 1 Plug the number into the area of a square formula: s^2
              8^(2 )=64 units^2




You can also find the area of a square using the diagonals. The diagonal of a square divides the square into two 45-45-90 triangles. You can use the rules of this special right triangle in order to find a missing side, and then use the area of a square formula. See the example problem below.



Example 2 Find the area of a square with a diagonal of 14 units.









Step 1. The diagonal bisects the ninety degree angle, and creates a 45-45-90 triangle. We can use the rules of a 45-45-90 triangle to find the length of one side.

Step 2. Following the rules of a 45 45 90 the leg equals x, and the hypotenuse equals x√2

Step 3. Plug in the information provided. The hypotenuse length equals 14 units, therefore I will have.



Step 4. Solve for x by dividing by the √2






Step 5.Now we plug s into our area of a square formula for a square s^2







Finding the diagonal length of a square, from side length.

The formula for side length equals  side length√2

Find diagonal length of a square if the side length equals 4 units.

Plug your information into the diagonal formula, side√2

4√2 = 5.65 units


If a square has a side length of 34 units,what is the diagonal length?

34√2 =48.08 units

Finding the area of a square using the diagonals

square has four equal sides, four right angles, and the diagonals divide a square into 45-45-90 triangles.
The area of a square can be found using length times width, but because a square has four equal sides, you can use s^2. (s = length of one side)

Common Core Standard  6.G.1 , 7.G.6  6th Grade Math    7th Grade Math
Questions answered in this video
  • How do you find the area of a square?
  • What is the formula for finding a squares area?
  • How do you find area of a square if you are only given the diagonal?
  • In a right triangle,how do you find the hypotenuse?

Finding the area of a square video tutorial

header moomoomath quick homework help
header moomoomath quick homework helpheader moomoomath quick homework helpheader moomoomath quick homework help
header moomoomath quick homework help
s = 7 square root 2
14= x square root 2

Area of a square formula

7 square root 2
square with 8 side
area of a square using diagonals

The area of a square formula equals s^2

square/area of a square formula
S
S

How to find the area of a square using the area of a square formula.

s = side of the square

What is area?

 Area is the size of a surface. Think of area as how much paint it would take to cover the surface. For plane shapes you can calculate area using a formula. Here is a list of the area formulas of plane shapes. Irregularly shaped objects are not as straight forward, and sometimes take some creativity to calculate the area. For instance how could you calculate the area of object A ?
object a
object a split into shapes
=
In this instance you could break it into two or three common shapes.
Sometimes you can use coordinates to find the area, or even count squares.

Object A

Area of a square calculator

The diagonals of a square can also be used to find the area. The diagonals of a square bisect each other, which results in four half diagonals that are congruent. The diagonals create four congruent isosceles triangles.The diagonals of a square create two 45-45-90 right triangles.