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# Surface Area of a Square

## Finding the area of a square video tutorial

• 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?

## 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 ?

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.

# Area of a square formula

## Common Core Standard 6.G.1 , 7.G.6 6th Grade Math 7th Grade Math

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)

## s = side of the square

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.

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

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

## Finding the area of a square using the diagonals

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