Square is a closed two-dimensional figure with four sides and four corners. The length of all four sides is equal and parallel to each other.
A square is a quadrilateral in which:
- The opposite sides are parallel.
- All four sides are equal.
- All angles measure 90°.
Area of a Square
Area of a square is the space enclosed within its boundary. It is given by the product of any of its two sides and denoted in sq. units. By formula, we have,
Area of a square = Side × Side
Let us assume the side of the square to be equal to S.
Therefore,
Area = S2.
Area of a triangle
A triangle is a two dimensional-figure enclosed within three sides, which may or may not be of equivalent length. The area is considered to be the space contained within the three sides. The height of the triangle connects the apex to the mid point of the base of the third side. Now.
Let us assume h to be the height and b the base of the triangle,
Therefore,
Area = 1/2 × base × height
= 1/2 × b × h
Area of a rectangle
The area of a rectangle is the space enclosed within its boundary. It is given by the product of any of its length and breadth and denoted in sq. units. By formula, we have,
Area of a rectangle = Length x Breadth
Let us assume the length of the rectangle to be equal to l and b to be breadth.
Therefore,
Area = length × breadth.
Which figure encloses more area: a square of side 2 cm a rectangle of side 3 cm and 2 cm a triangle of side 4 cm and height 2 cm?
Solution:
According to the formulae computed above, we have,
Area of a square = (side)2.
Here
Side = 2 cm
Therefore, Area = 22 cm2
= 4 cm2 …..I
Area of rectangle = length x breadth
We have,
length = 3 cm
breadth = 2 cm
Therefore, Area = 3 × 2 cm2
= 6 cm2 …..II
And, area of triangle = 1/2 × Base × Height
= 1/2 × 4 × 2 cm2
= 4 cm2…. III
Therefore, on comparing, we have,
Area of rectangle > Area of square = Area of triangle
Similar Questions
Question 1: Calculate which shape encloses more area;
Square with sides 10 m,
Rectangle with 11 m length and 10 m breadth,
Triangle with height 20 m and base 11 m
Solution:
As we know that
I. Area of square = Side × Side
Area of square = Side2
Given : Side of square is 10 m
Area of square = 102
Area of square = 10 × 10
Area of square = 100 m2
II. Area of rectangle = Length × Breadth
Given : Length is 11 m and Breadth is 10 m
Area of rectangle = 11 × 10
Area of rectangle = 110 m2
III. Area of triangle = 1/2 × Base × Height
Given : Base is 11 m and Height is 20 m
Area of triangle = 1/2 × 11 × 20
Area of triangle = 110 m2
Therefore From I, II and III we get;
Area of square = 100 m2
Area of rectangle = 110 m2
Area of triangle = 110 m2
Thus,
Area of Rectangle = Area of triangle > Area of square.
Question 2: Calculate in these of the shape which shape will enclose more area?
Circle having radius 20 cm (Use π = 3.14)
Parallelogram having base of 40 cm and height of 30 cm
Trapezium having parallel side 15 cm and 20 cm and height 40 cm
Solution:
I. Area of circle = πr2
Given : Radius is 20 cm
Area of circle = 3.14 × 20 × 20 (Using π = 3.14)
Area of circle = 1256 cm2
II. Area of parallelogram = Base × Height
Given : Base is 40 cm and Height is 30 cm
Area of parallelogram = 40 × 30
Area of parallelogram = 1200 cm2
III. Area of trapezium = 1/2 × (Sum of parallel sides) × Height
Given : Height is 40 cm and Parallel side are 15 cm and 20 cm
Area of trapezium = 1/2 × (15 + 20) × 40
Area of trapezium = 700 cm2
Therefore,
Area of circle (1256 cm2) > Area of parallelogram (1200 cm2) > Area of trapezium (700 cm2).
Question 3. Find which figure has maximum perimeter?
Square of sides 50 m
Rectangle of length 65 m and breadth 30 m
Equilateral triangle of side 65 m
Solution:
Here,
I. Perimeter of square = 4 × Side
Given : Side is 50 m
Perimeter of square = 4 × 50
Perimeter of square = 200 m
II. Perimeter of rectangle = 2 × (Length + Breadth)
Given : Length is 65 m and breadth is 30 m
Perimeter of rectangle = 2 × (65 + 30)
Perimeter of rectangle = 2 × 95
Perimeter of rectangle = 190 m
III. Perimeter of Equilateral triangle = Side + Side + Side
Given : Side is 65 m
Perimeter of Equilateral triangle = 65 + 65 + 65
Perimeter of Equilateral triangle = 195 m
Therefore,
Perimeter of square = 200 m > Perimeter of Equilateral triangle = 195 m > Perimeter of rectangle = 190 m.
Question 4. Find how many small square of side 2 m and be formed from a large square of side 8 m?
Solution:
As we know that,
Area of square = Side × Side
Area of large square = 8 × 8
Area of large square = 64 m2
Now,
Area of small square = Side × Side
Area of small square = 2 × 2
Area of small square = 4 m2
Further finding how many small squares can be formed from the large square
⇒ Area of large square/Area of small square
⇒ 64/4
⇒ 16 times
Therefore,
16 small square can be formed from a large square.