Squares

Background

Let's talk about squares...

Question

What is the definition of a square? What is its perimeter? What is its area?

Answer

A square is a plane figure that has four equal sides and four right angles.

Perimeter is the sum of its edges. Since each edge is equal, we can say the perimeter = 4s, where s is the measure of one side.

Area is the space enclosed within the perimeter. Area is the base times the height, but since they are equal, we can say that A = s^2  

Analysis

Squares are one of the first geometric shapes we learn in school. It looks like this:



The perimeter is the sum of the sides. Notice in this example that each side is a measure of 1 unit. Therefore, the perimeter is 4 units:

1 + 1 + 1 + 1 = 4 (1) = 4 units

Since each side is equal, we can say the Perimeter = 4s, where s is a side of the square.

The area is the space the perimeter encloses. We can either count squares with sides of 1 (there's 1 in our diagram), or we can multiply the "bottom" side by the "side". Since both of these are 1, we end up with:

Area = base x height = 1 x 1 = 1^2 = 1 square unit

Since the base and height are equal, we can say the Area = s^2

Vocabulary used:

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Where might you have come from?

Fact-orials Index

Geometry:

• Perimeter and Area

Where might we go?

Numbers:

• Pi