Rectangles

Rectangle
Definition

Rectangle
Geometric figures have several classifications, one is based on the number of sides it has. A figure with four sides [four angles] is called a quadrilateral. The rectangle is a quadrilateral with four right angles and opposite sides equal. The sides are usually referred to as length and width or base and height. The rectangle is probably the most comman and useful quadrilateral.

Perimeter

Rectangle
The distance around any geometric polygon [figure with straight sides] is the sum of its sides.

For a rectangle that would be:
P = L + W + L + W or
P = 2L + 2W.

The perimeter of the rectangle below is:

Rectangle
P = 2L + 2W
P = 2(8) + 2(4)
P = 16 + 8
P = 24 cm

We would be using perimeter to frame a painting or buy fencing or calculate how far it is to walk around the gym. Perimeter is 1-dimensional and is measured in linear units such as inches, feet or meters.

Yard with Fence

Area

The area of a rectangle is the number of square units inside the rectangle.
Rectangle
To calculate the number of squares, multiply the the number of columns [Length or Base] by the number of rows [Width or Height.]

A = LW
A = 5 X 3
A = 15 sq

Area is 2-dimensional: it has a length and a width. Area is measured in square units such as square inches, square feet or square meters.

We would be using area to calculate how much carpet to buy for a room or how much wall paper or paint is needed for the walls.

The Golden Ratio

Golden Rectangle
The golden rectangle has the property that when a square is removed a smaller rectangle of the same shape remains. Thus a smaller square can be removed, and so on, with a spiral pattern resulting.

The golden rectangle is a rectangle whose side lengths are in the golden ratio, which is approximately 1.618 and represented by the Greek letter phi. The common 3 X 5 card comes pretty close to this ratio.
Greek letter phi
Some artists and architects believe the Golden Ratio makes the most pleasing and beautiful shape. Many buildings and artworks have the Golden Ratio in them, such as the Parthenon in Greece.

The Parthenon

Self Quiz

1. A 2-meter wide path is constructed around the outside of a rectangular garden that is 50 m by 100 m.

Rectangle
What is the area of the garden?
2. What is the perimeter of the garden?
3. What is the area of the pathway?

Answers

1. 5000 sq m
2. 300 m
3. 616 sq m

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