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Math - Geometry Lesson Plans : Perimeter & Area of Rectangles & Squares 

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Mensuration - Formulae for Perimeter and Area of Rectangles and Squares
 

A quadrilateral is a polygon which has four sides.
A rectangle is a quadrilateral which has four right angles.
A square is a rectangle which has four equal sides.


quadrilateral : rectangle

Perimeter of a rectangle = 2 (Length + Breadth)
Any one of the two longer sides of a rectangle is its length.
In the figure alongside of the rectangle PQRS, length = PQ = RS.
Any one of the two shorter sides of a rectangle is its breadth.
In the figure alongside of the rectangle PQRS, breadth = QR = PS.
In the figure alongside of the rectangle PQRS, perimeter = 2 (PQ + QR).

Example
Find the perimeter (in cm) of a rectangle whose length is 8 cm and breadth is 4 cm.
Solution. Perimeter of a rectangle = 2 (Length + Breadth)
= 2 (8 + 4) = 24 cm.


quadrilateral : rectangle

In the figure alongside of the rectangle PQRS, diagonal = QS = PR (shown in dashed line)

 

= Ö

PQ2 + QR2
(by Pythagorean Theorem applied to ΔPQR).

 

Diagonal of a rectangle = Ö

Length2 + Breadth2

 

Example
Find the diagonal (in cm) of a rectangle whose length is 12 cm and breadth is 5 cm.
Solution.

Diagonal of a rectangle = Ö

Length2 + Breadth2
= Ö

122 + 52
= 13 cm.


quadrilateral : rectangle

Area of a rectangle = Length × Breadth
In the figure alongside of the rectangle PQRS, area = PQ × QR.

Example
Find the area (in cm2) of a rectangle whose length is 10 cm and breadth is 5 cm.
Solution. Area of a rectangle = Length × Breadth
= 10 × 5 = 50 cm2.



quadrilateral : square

Perimeter of a square = 4 × Side
In the figure alongside of the square PQRS, side = PQ = QR = RS = PS.
In the figure alongside of the square PQRS, perimeter = 4 × PQ.

Example
Find the perimeter (in cm) of a square whose side is 5 cm.
Solution. Perimeter of a square = 4 × Side
= 4 × 5 = 20 cm.


quadrilateral : square

Diagonal of a square = Ö2 Side

= Ö

PQ2 + QR2
(by Pythagorean Theorem)

 

= Ö

PQ2 + PQ2
= Ö

2 PQ2
= Ö2 PQ.

 

In the figure alongside of the square PQRS, diagonal = QS = PR (shown in dashed line)

 

Example
Find the diagonal (in cm) of a square whose side is 15Ö2 cm.
Solution. Diagonal of a square = Ö2 Side
= Ö2 × 15Ö2 = 30 cm.


quadrilateral : square

Area of a square = Side2
In the figure alongside of the square PQRS, area = PQ2.

Example
Find the area (in cm2) of a square whose side is 5 cm.
Solution. Area of a square = Side2
= 52 = 25 cm2.


quadrilateral : square

Area of a square = ½ × Diagonal2
In the figure alongside of the square PQRS, area = PQ2 = (PR / Ö2)2 = ½ × PR2.

Example
Find the area (in cm2) of a square whose diagonal is 6 cm.
Solution. Area of a square = ½ × Diagonal2
= ½ × 62 = 18 cm2.


Math - Geometry Lesson Plans : Practice Exercise for Perimeter & Area of Squares & Rectangles

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