Area of a Square
In area of a square we will learn how to find the area by counting squares.
To find the area of a region of a closed plane figure, we draw the figure on a centimeter squared paper and then count the number of squares enclosed by the figure.
We know, that square is a rectangle whose length and breadth are equal. In a square all four sides are equal.
Therefore, area of a square = (side × side) square units = (side)^{2} square units.
In a square the length is equal to breadth.
Hence, area of a square = side × side
The number of 1 cm squares enclosed = 4
Area = 4 sq cm
4 = 2 × 2
Hence, area = side × side
The unit of sides and the corresponding units of areas as given below:
Unit of Side

Unit of Area

mm

square mm (sq mm) or mm^{2}

cm

square cm (sq cm) or cm^{2}

m

square m (sq m) or m^{2}

km

square km (sq km) or km^{2}

Note: Write finding the area of a given figure, make sure that the sides (length or breadth) are in the same unit of length. If they are given in different units, change them to the same unit.
Look at the above figure. You can see that the area of a square having sides 2 cm each is equal to the area of 4 squares of sides 1 cm each = 4 cm^{2}. It can also be expressed as 2 cm × 2 cm = 4 cm^{2}. Area of a square is 2 times of its each side.
Solved examples to find the area of a square when side is given:
1. Find the area of a square of side 8 cm.
Area of a square = length (l) × length (l)
= 8 × 8 sq. cm.
= 64 sq. cm.
2. Find the area of a square of side 11 m.
Area of a square = length × length
= 11 × 11 sq. m.
= 121 sq. m.
3. Find the area of a square of side 49 cm.
Area of a square = length × length
= 49 × 49 sq. cm.
= 2401 sq. cm.
4. Find the area of a square of side 50 m.
Area of a square = length × length
= 50 × 50 sq. m.
= 2500 sq. m.
5. Find the area of a square photo frame whose side is 20
cm.
Area of the photo frame = 20 cm × 20 cm
=
400 sq. cm
Questions and Answers on Area of a Square:
1. Find the area of the squares with the given side.
(i) 4 cm
(ii) 2.5 cm
(iii) 8 m
(iv) 90 mm
(v) 13.4 km
Answers:
(i) 16 sq. cm
(ii) 6.25 sq. cm
(iii) 64 sq. m
(iv) 8100 sq. m
(v) 179.56 sq. km
2. Find the area of the squares whose side is:
(i) 4 cm
(ii) 20 cm
(iii) 6 m
(iv) 200 m
(v) 12 cm
(vi) 40 cm
Answers:
(i) 16 sq. cm
(ii) 2500 sq. cm
(iii) 36 sq. m
(iv) 40000 sq. m
(v) 144 sq. cm
(vi) 1600 sq. cm
Word Problems on Area of a Square:
3. The area of a badminton court is 140 square m. If the
breadth of the court is 7 m, then find its length.
Answer:
20 m
4. The display board of class VII A is in the shape of a
square. If the length of its side is 60 cm, then find its area.
Answer:
3600 sq. cm
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● Area.
Area of a Rectangle.
Area of a Square.
To find Area of a Rectangle when Length and Breadth are of Different
Units.
To find Length or Breadth when Area of a Rectangle is given.
Areas of Irregular Figures.
To find Cost of Painting or Tilling when Area and Cost per Unit
is given.
To find the Number of Bricks or Tiles when Area of Path and Brick
is given.
Worksheet on Area.
Worksheet on Area of a Square and Rectangle
Practice Test on Area.
5th Grade Geometry
5th Grade Math Problems
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