# Rectangle: Definition, Area, Perimeter, Diagonal, Properties, & Examples

One type of shape in geometry is rectangle. There are many rectangle-shape things in daily life for example table, whiteboard, books, phone, door, window, etc.

## Definition of Rectangle

Rectangle is one of a two-dimensional shape in geometry. It has two (pairs) parallel sides that they are two lengths and two widths. The length and width have different size. It also has four right angles (90°). Because of it has four right angles then total angles is 360°.

Another name of rectangle is equiangular quadrilateral.

Important concept is rectangle is one of parallelogram, but not all of parallelogram are rectangle. Besides that, every square is a rectangle but rectangle is not a square.

## Area of a Rectangle

Area of a rectangle depends on the length (l) and width (w).

Area = A = l x w

## Perimeter of a Rectangle

Perimeter of a rectangle is the sum of all the sides. Because of there are two parallel lines that called length and width sides, then

Perimeter = P = sum of all sides = l + l + w + w = 2 (l + w)

Diagonal of a Rectangle

Diagonal of a rectangle means a line that connect one of the corners with the opposite. Rectangle has four corners. It means that it has two diagonals. If there is rectangle ABCD then

The diagonal of rectangle ABCD are AC and BD. They are same length, AC = BD.

The diagonals intersect each other in middle of the line. Let O as the center, then AO = CO, BO = DO, AO = DO, and BO = CO.

Determining length of diagonal (d) by using Pythagorean theorem.

d = √(l2 + w2)

A diagonal of a rectangle divides the rectangle into two congruent triangles. Two diagonals divide the rectangle into four congruent triangles.

## Properties of a Rectangle

There are properties of rectangle:

• It is two-dimensional shape.
• It has two (pairs) parallel sides: 2 length & 2 width
• Opposite sides of rectangle are parallel and equal.
• It has four right angles.
• It has two diagonals and they intersect each other in the middle of the line.
• Area of rectangle is product of the length and width.
• Perimeter of rectangle means sum of all sides.

## Examples

1. Calculate the area, perimeter, and the diagonal.

Length = 16

Width = 12

Then

Area = l x w = 16 x 12 = 192

Perimeter = 2 (l + w) = 2 (16 + 12) = 2 (28) = 56

Diagonal = √(l2 + w2) = √(162 + 122) = √(256+144) = √400 = 20

2. Determine the area and perimeter of a rectangle if diagonal is 10cm and the length is 8.

Diagonal = 10 cm

d = √(l2 + w2)

10 = √(82 + w2)

102 = 64 + w2

100 = 64 + w2

w2 = 100 – 64

w2 = 36

w = 6cm.

then,

area = l x w = 8 x 6 = 48 cm2

perimeter = 2 (l+w) = 2(8+6) = 2(14) = 28 cm.

3. George will make a fence in around of the house. He only knows that the area is 80m2 and the length is two meters more than the width. If the price of 1 m fence is 12 dollars, how much he must pay to make all the fence?

Area = 80 m2

Let width = w

length = l = w+2

Then

Area = l x w

80 = (w+2) x w

80 = w2 + 2w

w2 + 2w – 80 = 0

(w+10)(w-8) = 0

w = -10 (impossible) or w = 8 m

So, the length = w + 2 = 8 + 2 = 10 m

knowing total fence means knowing the perimeter.

Perimeter = 2 (l+w)

= 2 (10 + 8)

= 2 (18)

= 36 m

How much the total price?

Total price = price of fence 1 m x total fence

= 12 x 36

= 432 dollars.