How to find the area of a **square** ?

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

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.

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

Let’s look at an example 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

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