# Rectangle

## Definition

A plane figure with four straight sides making four right internal angles.

## Properties

1. Has four sides and four angles; in â–­ ABCD, AB, BC, CD, and DA are four sides and âˆ ABC, âˆ BCD, âˆ CDA, âˆ DAB are four angles
2. Opposite sides are equal; so AB = CD and BC= DA
3. Opposite sides are parallel; AB âˆ¥ CD and BC âˆ¥ DA
4. All the angles are 90Â°; in â–­ ABCD, âˆ ABC = âˆ BCD = âˆ CDA =âˆ DAB =  90Â°
5. The diagonals are equal and bisect each other; so AC = BD
6. The sum of the interior angles is equal to 360 degrees; âˆ ABC + âˆ BCD + âˆ CDA  + âˆ DAB = 360Â°

## Formulas

### Diagonal

The line segments linking opposite vertices or corners of the rectangle. The formula is given below:

Diagonal (D) = âˆšw2 + l2, here w = width, l = length

Problem: Finding the diagonal of a rectangle when the WIDTH and LENGTH are known

Find the diagonal of a rectangle whose width is 12 cm and length is 5 cm.

Solution:

As we know,
Diagonal (d ) = âˆš(w 2 + l 2), where w = 12 cm and l = 5 cm
= âˆš(122 + 52)
=âˆš(144 + 25)
= âˆš169
= 13 cm

### Area

The total space enclosed by the rectangle. The formula is given below:

Area (A) = w Ã— l, here w = width, l = length

Problem: Finding the area of a rectangle when the WIDTH and LENGTH are known

Find the area of a rectangle whose width is 10 cm and length is 6 cm.

Solution:

As we know,
Area (A) = w Ã— l, where w = 10 cm and l = 6 cm
= 10 Ã— 6 cm
= 60 cm2

### Perimeter

The total distance covered around the edge of the rectangle. The formula is given below:

Perimeter (P) = 2(w + l), here w = width, l = length

Problem: Finding the perimeter of a rectangle when the WIDTH and LENGTH are known

Find the perimeter of a rectangle whose width is 7 cm and length is 9 cm.

Solution:

As we know,
Perimeter (P ) = 2 (w + l ), wherew = 7 cm and l = 9 cm
= 2(7 + 9) cm
Â = 2 Ã— 16 cm
= 32 cm

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