In this section we will discuss about Area of Square.

The formulas related to the above topic are as follows

Let ‘a’ be the length of each side of a square. Then,

**• ** Perimeter = 4a units

**• ** Area = a ^{2} =( Perimeter/4) ^{2} sq. units

**•** Area = ½ (Diagonal) ^{2} sq.units

**•** Side of the square = √(Area) unit

**•** Diagonal = √ a unit

**Some solved examples on Area - Perimeter of Square **

1) Find the area and perimeter in square centimeters, of a square whose side is (i) 2.4 dm (ii) 20 mm

(i) We have,

1 dm = 10 cm

Side of the square = 2.4 dm = (2.4 x 10) cm = 24 cm

Area of the square = (side)^{2}

= 24^{2}

= 576 cm^{2}

Perimeter of the square = 4 x side

= 4 x 24

= 96 cm

(ii) We have,

1 mm = 0.1 cm

Side of the square = 20 mm = (20 x 0.1) cm = 2 cm

Area of the square = (side)^{2}

= 2^{2}

= 4 cm^{2}

Perimeter of the square = 4 x side

= 4 x 2

= 8cm

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2) Find the area of a square park whose perimeter is 320 m.

**Solution : **

Area = (Perimeter/ 4)^{2} sq. units

Area = (320/ 4)^{2}

= (80)^{2}

∴ Area of a square park = 6400^{2}

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3) The side of a square is 4 cm. Find the area of the triangles formed by joining all of its diagonals.

**Solution : **

Side = 4 cm

Area of square = (side)^{2} = 16 cm ^{2} .

Area of triangle formed by joining two of its diagonals

= ¼ of 16 = 4 cm^{2}

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4) A path 1m wide is built along the border inside a square garden of side 30 m. Find (i) the area of the path (ii) the cost of planting the grass in the remaining portion of the garden at the rate of $40 per sq.m.

**Solution : **

ABCD is the square garden of side 30 m.

PQRS is the region inside the garden.

PQ = (30 -1-1 ) = 28 m

PS = ( 30 – 1 – 1 ) = 28 m

(i) Area of the path = Area of ABCD – Area of PQRS

= ( 30 x 30) – 28 x 28)

= 900 – 784

Area of path = 116 sq.m

(ii) Area of the remaining portion in which the grass is planted = Area of square PQRS

= 28 x 28

= 784 sq.m

∴ cost of planting the grass in the region PQRS = $ ( 764 x 40) = $ 31,360

**Mensuration : Area and Perimeter **

• Perimeter and Area of Irregular Shape

• Area and Perimeter of the Rectangle

• Area of Square (perimeter of square)

• Perimeter of Parallelogram(Area of Parallelogram)

• Area of Rhombus(Perimeter of rhombus)

• Area of Trapezoid (Trapezium)

• Triangle Area (Perimeter of triangle)

• Herons Formula

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The formulas related to the above topic are as follows

Let ‘a’ be the length of each side of a square. Then,

1) Find the area and perimeter in square centimeters, of a square whose side is (i) 2.4 dm (ii) 20 mm

(i) We have,

1 dm = 10 cm

Side of the square = 2.4 dm = (2.4 x 10) cm = 24 cm

Area of the square = (side)

= 24

= 576 cm

Perimeter of the square = 4 x side

= 4 x 24

= 96 cm

(ii) We have,

1 mm = 0.1 cm

Side of the square = 20 mm = (20 x 0.1) cm = 2 cm

Area of the square = (side)

= 2

= 4 cm

Perimeter of the square = 4 x side

= 4 x 2

= 8cm

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2) Find the area of a square park whose perimeter is 320 m.

Area = (Perimeter/ 4)

Area = (320/ 4)

= (80)

∴ Area of a square park = 6400

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3) The side of a square is 4 cm. Find the area of the triangles formed by joining all of its diagonals.

Side = 4 cm

Area of square = (side)

Area of triangle formed by joining two of its diagonals

= ¼ of 16 = 4 cm

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4) A path 1m wide is built along the border inside a square garden of side 30 m. Find (i) the area of the path (ii) the cost of planting the grass in the remaining portion of the garden at the rate of $40 per sq.m.

ABCD is the square garden of side 30 m.

PQRS is the region inside the garden.

PQ = (30 -1-1 ) = 28 m

PS = ( 30 – 1 – 1 ) = 28 m

(i) Area of the path = Area of ABCD – Area of PQRS

= ( 30 x 30) – 28 x 28)

= 900 – 784

Area of path = 116 sq.m

(ii) Area of the remaining portion in which the grass is planted = Area of square PQRS

= 28 x 28

= 784 sq.m

∴ cost of planting the grass in the region PQRS = $ ( 764 x 40) = $ 31,360

• Perimeter and Area of Irregular Shape

• Area and Perimeter of the Rectangle

• Area of Square (perimeter of square)

• Perimeter of Parallelogram(Area of Parallelogram)

• Area of Rhombus(Perimeter of rhombus)

• Area of Trapezoid (Trapezium)

• Triangle Area (Perimeter of triangle)

• Herons Formula

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