Thursday, May 9, 2013

How to find the area of a square.

How to find the area of a square ?

Please watch the video if you need to watch the problems being solved

Area of a square

 

Let’s begin with the formula for area of a square is s^2   s=side

 Example 1 Find the area of a square with a side of 8 units. 

 

 

area of a square

Step 1 Plug the number into the formula: 8^(2 )=64 units^2

Let’s look at an example using diagonals.

 

 

area of square using diagonals

 

 

 

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. The leg lengths of a 45-45-90 triangle equals x and the hypotenuse equals x√2

 

Step 3. In order to get x by itself I will take the hypotenuse length of the 45-45-90 triangle that the diagonal creates 14 and set it equal to x root 2 which looks like

14=x√2 

 

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

14/√2=(x√2)/√2 =7√2 = S

 

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

 

Step 6. (7√(2 ) )^2 = 42 x2 =98 units^2