Geometry

Perimeter

• The perimeter is the distance around a two-dimensional object.

• The perimeter of a polygon can always be calculated by adding all the length of the sides together.

Perimeter Square = 4S

• The perimeter of a square is the distance around the outside of the square. A square has four sides of equal length.

• The formula for finding the perimeter of a square is:

4S (Length of a Side)

Perimeter Square

Example:

Find the perimeter of a square with sides that measure 25 m.

Solution:

P = 4S

P = 4 (25m)

P = 100 m

So, the perimeter is 100 m.

Perimeter Rectangle

2L + 2W

or

2 (L + W)

L = Length

W= Width

Perimeter Rectangle

Example:

Find the perimeter of a rectangular field of length 45 m and width 35 m.

Solution:

P = 2 (L + W)

P = 2 (45 + 35)

P = 2 (80)

P = 160

So, the perimeter is 160 m.

Circumference Circle

Circumference   =   2π r  Circumference = π d

• P stands for the perimeter, • r stands for the radius • π is the mathematical constant pi (π =

3.14159265...) • d stands for the circle's diameter (twice the radius

of a circle)

Circumference Circle

Circumference

Example:

The diameter of a circle is 3 centimeters. What is the circumference?

Circumference = π d = 3.14 · (3 cm) 

= 9.42 cm

Area

• Area is a count of how many unit squares fit inside a figure.

• The solution is labeled using square units.

Area of a Square

The area A of any square is equal to the square of the length s of a side.

Formula: A = s2

Area of a Rectangle

• The area A of any rectangle is equal to the product of the length l and the width w.

Formula: A = lw or A = bh

Area of a Triangle

• The area A of any triangle is equal to one-half the product of any base b and corresponding height h.

Formula: A = 1/2bh

Area of a Trapezoid

• The area A of any trapezoid is equal to one-half the product of the height h and the sum of the bases, b1 and b2.

Formula: A = 1/2h(b1 + b2)

Area of a Circle

• The area A of any circle is equal to the product of PI and the square of the radius r.

Formula: A = (PI)r2