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. The basic figure of a square is shown below. A square is a quadrilateral in which: - The opposite sides are parallel.
- All four sides are equal.
- All angles measure 90°.
Perimeter of the square The length of the boundary of a square can be calculated by performing the summation of all its sides, which is given by, Perimeter of a square = side + side + side + side. Therefore, Perimeter of Square = (4 × Side) units If the side of a
square is 10 cm then how many times will the new perimeter become if the side length is doubled?Solution: Here we will be finding how many times the perimeter of a square will be changed if we double the sides of the square Perimeter of a square = Side + Side + Side + Side Perimeter of a square = 4 × Side Here we have the side of the square = 10 cm Putting the value of the side of square in the perimeter of a square formula Perimeter of a square = 4 × 10 Perimeter of a square = 40 cm ………….(1) When the side of the square is doubled The side of the new square becomes 2 × 10 cm =
20 cm Perimeter of the new square = 4 × Side Perimeter of the new square = 4 × 20 Perimeter of the new square = 80 cm ……….(2) Now we will be finding the change in the perimeter after increasing the side of the square Perimeter of the
original square = 40 cm (from 1) Perimeter of the new square = 80 cm (from 2) To find the increase in the perimeter Subtract (1) from (2) Increase in Perimeter = Perimeter of the new square – Perimeter of the original square ⇒ Increase in Perimeter = 80 – 40 ⇒ Increase in Perimeter = 40 cm To find how many times the perimeter is increased Increase in the perimeter = Increase in the perimeter = Increase
in the perimeter = 2 times Therefore, We can see that the perimeter of the new square is double the perimeter of the original square Thus, The perimeter of a square is increased by 2 times when its sides are doubled.
Similar QuestionsQuestion 1. If the side of a square is 20 cm and its sides are tripled find how many times the new perimeter is increased? Solution: Here
we have to find how many times the perimeter will be increased if the side of the square is tripled As we know that Perimeter of a square = 4 × side Given : Side of the square is 20 cm Perimeter of a square = 4 × 20 Perimeter of a square = 80 cm Further, When the side of the square is tripled Side of the new square = 3 × 20 Side of the new square = 60 cm Now, Perimeter of the new square = 4 × side Perimeter of the new square
= 4 × 60 Perimeter of the new square = 240 cm Further we will find the increase in perimeter Increase in Perimeter = Perimeter of the new square – Perimeter of the original square Increase in Perimeter = 240 – 80 Increase in Perimeter = 160 To find how many times the perimeter is increased Increase in the perimeter = Increase in the perimeter = Increase
in the perimeter = 3 times Therefore, We can see that the perimeter of the new square is triple the perimeter of the original square Thus, The perimeter of a square is increased by 3 times when its sides are tripled.
Question 2. Find how many times the perimeter of a square will decrease if the side of the square is reduced by half. The side of the original square is 50 cm? Solution: Here we have
to find how many times the perimeter will be reduced if the side of the square is halved. As we know that Perimeter of a square = 4 × side Given: Side of the square is 50 cm Perimeter of a square = 4 × 50 Perimeter of a square = 200 cm Further, When the side of the square is halved Side of the new square = Side of the new square = 25 cm Now, Perimeter of the new square = 4 × side Perimeter of the new square = 4 × 25 Perimeter of the new square = 100 cm Further we will find the decrease in perimeter Increase in Perimeter = Perimeter of the original square –
Perimeter of the new square Decrease in Perimeter = 200 – 100 Decrease in Perimeter = 100 cm To find how many times the perimeter is decreased in the perimeter = Decrease in the perimeter
= Decrease in the perimeter = 2 times Therefore, We can see that the perimeter of the new square is reduced by 2 times the perimeter of the original square Thus, The perimeter of a square is reduced to half when its sides are halved.
Question
3. If the perimeter of a square is increased by four times, then find how many times the side of the new square is increased. The perimeter of the original square is 160 cm? Solution: Here we have to find the increase in the side of the square when its perimeter is increased by four times As we know that Perimeter of a square = 4 × side Given: Perimeter of the original square is 160 cm Perimeter of the original square =
160 cm Perimeter of the original square = 4 × side 160 = 4 × side Side = Side of the original square = 40 cm Further, Perimeter of the original square is increased by four times Perimeter of the new square = 4 × 160 Perimeter of the new square = 640
cm Perimeter of the new square = 4 × side 640 = 4 × side Side = Side = 160 cm Side of the new square = 160 cm Now, Side of the original square = 40 cm Side of the new square = 160 cm Increase in side = Side of the new square – Side of the
original square Increase in Perimeter = 160 – 40 Increase in Perimeter = 120 cm To find how many times the side is increased Increase in the side = Increase in the perimeter = Increase in the perimeter = 4 times Therefore, We can see that the side of the new square is increased by four times the side of the original square Thus, The side of a square is increased by four times when its perimeter is increased by four times.
Question
4. Find the perimeter of the square is its area is 25 cm2? Solution: Here we have to find the perimeter of the square by the given area. Given: Area of the square is 25 cm2. As we know that Area of the square = Side × Side 25 = s × s s2 = 25 s = s = 5 cm Side of the square is 5 cm Further, Perimeter of the square = 4 × side Perimeter of the square = 4 × 5 Perimeter of the square = 20 cm Therefore, Perimeter of the square is 20 cm if its area is 25 cm2.
Question 5. If
the side of a square is increased by 2 times, then find how many times the area of the new square will be. The side of the original square is 10 cm. Solution: Here we have to find how many times the area will be increased if the side of the square is doubled As we know that Area of a square = side × side Given: Side of the square is 10 cm Area of a square = 10 × 10 Area of a square = 100 cm2 Further,
When the side of the square is doubled Side of the new square = 2 × 10 Side of the new square = 20 cm Now, Area of the new square = side × side Area of the new square = 20 × 20 Perimeter of the new square = 400 cm2 Further we will find the increase in area Increase in area = Area of the new square – Area of the original square Increase in Area = 400 – 100 Increase in Area = 300 To find how many times the area is
increased Increase in the area = Increase in the area = Increase in the area = 4 times Therefore, We can see that the area of the new square is 4 times the area of the original square Thus, The area of a square is increased by 4 times when its sides are doubled.
What happens to the area of a square when its side is halved?
Hence, It shows if side of square are halved, then its area become one-fourth.
Will the area of a square changes if its side is doubled by how many times?
The factor by which area of the square will change is 4 times the initial area.
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