Perimeter and area of polygons are introduced in this video. The difference between perimeter and area is explained. Hopefully your kids will have an easier time remembering this information if it’s put into a song!

For more help, check out our Lesson Page on Perimeter and Area of Polygons

Credit goes to: Flocabulary

## What Is Area?

Area is a fundamental concept in mathematics that measures the size of a two-dimensional shape or surface. It quantifies the amount of space enclosed within the boundary of a geometric figure. Whether it’s a simple shape like a square or a complex one like a polygon, understanding area is crucial in various fields including architecture, physics, engineering, and more.

The concept of area is intuitive and practical. For example, when you measure the floor space of a room to determine how much carpet you need, or when you calculate the area of a piece of land for construction purposes, you’re essentially finding its area. In mathematical terms, area is typically represented by square units, such as square meters, square centimeters, square inches, etc., depending on the units of measurement used.

The formula for calculating the area of basic geometric shapes is well-defined. Here are some common formulas:

**Square** – The area of a square is found by multiplying the length of one side by itself. If s represents the length of a side of the square, then the area A = s^{2}.

**Rectangle** – The area of a rectangle is calculated by multiplying its length by its width. If l represents the length and w represents the width, then the area A is given by A = l x w.

**Triangle** – The area of a triangle is found by multiplying its base by its height and then dividing by 2. If b represents the base length and h represents the height, then the area A is given by A = ½ b x h.

**Circle** – The area of a circle is given by the formula A = Π r^{2}, where r represents the radius of the circle and Π is a mathematical constant approximately equal to 3.14159.

**Trapezoid** – The area of a trapezoid is calculated by adding the lengths of its bases, multiplying the sum by the height, and then dividing by 2. If b_{1} and b_{2} represent the lengths of the two bases, and h represents the height, then the area A is given by A = ½ (b_{1} + b_{2}) x h.

These are just a few examples, but the concept of area extends beyond these basic shapes. For irregular shapes or more complex figures, finding the area might require more advanced techniques such as integration in calculus or breaking down the shape into simpler components whose areas can be calculated individually and then summed up.

One important property of area is that it is additive. This means that if a shape can be divided into two or more non-overlapping parts, then the total area of the shape is the sum of the areas of its parts. This property is often used to calculate the area of irregular shapes by breaking them down into simpler, easier-to-calculate parts.

## What Is Perimeter?

Perimeter is another fundamental concept in mathematics, particularly in geometry, that describes the length of the boundary of a two-dimensional shape or figure. Unlike area, which measures the space enclosed within a shape, perimeter focuses solely on the length of the outline or boundary.

When we talk about perimeter, we are essentially interested in finding the total distance around the outside of a shape. Imagine walking along the edge of a fence enclosing a garden; the total distance you cover is the perimeter of the garden. Similarly, if you were to trace the outline of a shape with a piece of string and then measure the length of that string, you would find the perimeter of the shape.

The concept of perimeter is applicable to various geometric shapes, from simple polygons like squares and rectangles to more complex figures like circles or irregular polygons. The method of calculating perimeter depends on the specific shape.

**Square** – In a square, all four sides are of equal length. Therefore, to find the perimeter, you simply multiply the length of one side by 4. If s represents the length of a side of the square, then the perimeter P is given by P = 4s.

**Rectangle **– A rectangle has two pairs of equal-length sides (opposite sides are equal). To find the perimeter, you add the lengths of all four sides. If l represents the length and w represents the width, then the perimeter P is given by P = 2l + 2w.

**Triangle** – In a triangle, the perimeter is simply the sum of the lengths of its three sides.

**Circle** – The perimeter of a circle is called the circumference. It is given by the formula C = 2 Π r, where r is the radius of the circle and Π is a mathematical constant approximately equal to 3.14159.

**Irregular Polygon** – For an irregular polygon, you would add up the lengths of all its sides to find the perimeter.

One important property of perimeter is that, unlike area, it is independent of the size or scale of the shape. For example, a square with side lengths of 3 units will always have a perimeter of 12 units (4 sides of length 3 each), regardless of whether those units are inches, centimeters, or any other unit of measurement.

Understanding perimeter is essential not only for geometric calculations but also for real-world applications such as fencing, construction, and determining the length of borders or boundaries. It provides a measure of the total distance around a shape and is a key concept in geometry and mathematical problem-solving.