What is Area?

http://www.mathsisfun.com/geometry/area.html

Area is the size of a surface!

Example:

These shapes all have the same area of 9:

Area of Simple Shapes

There are special formulas for certain shapes:

Example: What is the area of this rectangle?

The formula is:

Area = w × h
w = width
h = height

The width is 5, and the height is 3, so we know w = 5 and h = 3. So:

Area = 5 × 3 = 15

Read Area of Plane Shapes for more information.

Area of Difficult Shapes

To help you understand an area, imagine painting it and how much paint you might use.
You can sometimes break a shape up into two or more simpler shapes:

Example: What is the area of this Shape?

Let's break the area into two parts:

Part A is a square:

Area of A = a² = 20m × 20m = 400m²

Part B is a triangle. Viewed sideways it has a base of 20m and a height of 14m.

Area of B = ½b × h = ½ × 20m × 14m = 140m²

So the total area is:

Area = Area of A + Area of B = 400m² + 140m² = 540m²

Area by Adding Up Triangles

You can also break up a shape into triangles:

Then measure the base (b) and height (h) of each triangle:

Then calculate each area (using Area = ½b × h) and add them all up.

Area by Coordinates

If you know the coordinates of each corner point you can use the method explained in Area of Irregular Polygons:
There is an Area of a Polygon by Drawing Tool if you need it.

Area by Counting Squares

You can also put your shape on a grid and count the number of squares:

This rectangle has an area of 15

If each square was 1 cm on a side, then the area would be 15 cm² (15 square cm)

Sometimes the squares may not match the shape exactly, so you will need to "approximate" an answer.
One way is:

more than half a square counts as 1
less than half a square counts as 0

Like this:

This pentagon has an area of approximately 17

Or just use your eyes and count a whole square when the areas seem to add up, like with this circle, where the area marked "4" seems equal to about 1 whole square (also for "8"):

This circle has an area of approximately 14

Perimeter

Perimeter is the distance around a two-dimensional shape.

Example 1: the perimeter of this rectangle is 7+3+7+3 = 20

Example 2: the perimeter of this regular pentagon is 3+3+3+3+3 = 5×3 = 15

The perimeter of a circle is called the circumference:

Circumference = 2π × radius

Perimeter Formulas

		Triangle Perimeter = a + b + c
		Square Perimter = 4 × a a = length of side
		Rectangle Perimeter = 2 × (w + h) w = width h = height
		Quadrilateral Perimeter = a + b + c + d
		Circle Circumference = 2πr r = radius
		Sector Perimeter = r(θ+2) r = radius θ = angle in radians
		Ellipse Perimeter = very hard!