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In this lesson, we will learn about the area of a square.

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Consider this square. All the sides of this square have the same length, L.

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Now, we can get the area of this square, A, by multiplying both of these length L together.

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With this, we get the area, A, equals to L multiply by L. This gives L square.

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Note that, we also must include the unit. Since we are multiplying these 2 lengths together, the unit for the area will be in the form of square unit.

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We will see the explanations on this, in the upcoming example.

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Now, Let’s see some examples on using this formula.

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Find the area of this square when the length of each side is 3cm.

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To do so, we start with the formula for the area of a square, A equals to L square.

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Since the length of each side is 3 cm, we can substitute L with 3.

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This gives 3 square.

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Now, let's simplify 3 square. 3 square is actually the same as, 3 multiply by 3, which is 9.

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Let's write down this number.

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Now, this number is meaningless unless we include the unit for it.

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Since the length is given in centimeter, the unit for the area will be in square centimeter.

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Therefore, the area of this square is 9 square centimeter.

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Next example, given that the area of this square is 4 square feet, find the length of each side.

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Now, we start with the formula for the area of a square, A equals to L square.

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Since the value of the area is given, we can find the length of each side, by solving the equation for L.

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Here’s how. Since the area is given as 4 square feet, we can substitute A with 4.
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Now, we have, L square equals to 4.

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Let's rewrite this equation so that it will look neater.

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To find L, we can see that since 4 is equals to L square, L can be found by calculating the square root of 4.

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Square root of 4 is 2.

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Now this number has no meaning unless we include the unit for it.

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Since the area is given in square feet, the side of the square will be in feet.

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Therefore, the length of each side of the square is 2 ft.

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That is all for this lesson. Try out the practice question to further your understanding.