Perimeter: The perimeter of a shape is the distance around that shape. This distance may consist of straight lines or curves. We can find the perimeter by adding the lengths of these lines and curves together. The first example we’ll consider consists of straight lines only.

Example 1) Find the perimeter of the following shape:

To find the perimeter of this shape we’ll start in a corner and move clockwise around the shape adding the pieces until we reach the starting point again. Notice that in this shape some of the lengths are not given and have to be found.
 
 
 

P= 5 +3 + 6 + 7 + 8 + 2 + 3 + 12 = 46

 
 
 

As mentioned earlier we may have portions of circles as part of our shape. In order to find their lengths, we have to use the formula for the distance around a circle or the circumference of a circle.
 

C= 2r

Where "r" represents the length of the radius of the circle and  is a constant (approximately 3.14). In this course we will leave all answers in their exact form (i.e. in terms of ).
 
 

Example 2) Find the perimeter of the following shape:
 

This shape consists of two line segments, a quarter-circle, and a semi-circle. In addition to finding the length of the arcs, we also have to find the length of the missing part in the bottom segment.
 
 

Area:

The area of a shape is the number of 1 unit by 1 unit squares (square units) that can fit inside of a shape. If our shape is a rectangle or a square this number is easy to find. All we have to do is multiply the length and the width of the shape. But if our shape has slanted or curved parts, dividing it into smaller squares is not as easily accomplished. To find the area of such shapes we have to rely on formulas for the area of triangles and circles. The following table gives you the formulas for the area of some basic shapes.
 
 

Rectangle		A=bh
Triangle
Circle		A=r2

Now we can go back and find the area of the shape in example 2.

Example 3) Find the area of the following shape:
 

In order to find the area of this shape, we will divide it into three pieces; a rectangle (I), a semi-circle (II) and a quarter-circle (III). We will find the area of each piece separately and then find their sum.

 

I : A = 12´ 8 = 96

II : A = ½ (6²) = ½ (36) = 18 (We found ½ of the area of a full circle)

III: A= ¼ (8²) = ¼ (64) = 16 (We found ¼ of the area of a full circle)
 

Practice problems :

Find the Area and Perimeter for the following:

1. 

2. 

3. 
 
 

1.

Perimeter= 18 + +12 + = 18+3+12+3= 30+6

Area= = 9+72+4.5= 72+13.5

2.

Perimeter= 10 +12 + = 22 + 5

Area = 22 -  = 22 – 12.5 (Notice that in this case we have to subtract the areas, but the perimeter is still added. The perimeter is the distance around a shape and the fact that this shape curves inward does not make the distance any shorter.)

3.

Perimeter= 24 ++10+= 24 + 7 + 10 + 7 = 34 + 14

Area = + 70 + = 12.25 + 70 + 12.25 = 70 + 24.5