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.
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.
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.
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.
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.
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.
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.
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.
