Math & History: Intro to Area & Perimeter

I. Area

Area is the amount of space occupied by a flat (two dimensional) figure. It refers to the space inside the boundary or perimeter of a closed shape.

The area of a figure is the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, or square centimeters, square meters, etc.

Calculating Area

Let us see how to calculate the area of a shape with the help of a grid. The area of any shape is the number of unit squares that can fit into it. The grid is made up of many squares of sides 1 unit by 1 unit. Hence, each square is known as a unit square. Look at the figure shown below. Let us find the area of the shape drawn in the grid.

The area of this shape is the number of shaded unit squares.

Thus, the area of the shape = 9 square units.

Area of a Rectangle or Square

The area of a rectangle is the space occupied by it. Consider the yellow rectangle in the grid. It has occupied 6 units.

Area of rectangle

In the above example, the length of the rectangle is 3 units and the width is 2 units. Instead of counting the individual unit squares we can use the formula for finding the area of a rectangle.

Area of the rectangle = length × width

The area of a rectangle is obtained by multiplying its length and width which is the same as counting the unit squares. Thus, the formula for the area of a rectangle is: In this case, it will be 2 × 3 = 6 square units.

Area of a Square

The area of a square is the space occupied it. Look at the colored square shown in the grid below. It occupies 25 squares.

area of a square

From the figure, we can observe that the length of each side of the colored square is 5 units. Therefore, the area of the square, like the rectangle, is length x width which can be represented by the formula:

Area of a square = side × side

So, the area of this square = 5 × 5 = 25 square units.

Area and the Distributive Property

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Decomposing Shapes to Find Area

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II. Perimeter

Perimeter is the total length of the boundary of any closed shape. It is the distance around the outside of a two-dimensional shape.

Calculating Perimeter

The perimeter of a shape is determined by adding the length of all the sides enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.