1. Find the perimeter of each of the following figures:
1. Find the perimeter of each of the following figures:
Explanation:
(a) perimeter equals the total of all sides
= 1 + 2 + 4 + 5
= 12 cm
(b) Perimeter equals the total of all the sides
= 23 + 35 + 35 + 40
= 133 cm
(c) Perimeter equals the total of all sides
= 15 + 15 + 15 + 15
= 60 cm
(d) Perimeter equals the total of all sides
= 4 + 4 + 4 + 4 + 4
=20 cm
(e) Perimeter equals the total of all sides
= 1 + 4 + 0.5 + 2.5 + 2.5 + 0.5 + 4
= 15 cm
(f) Perimeter equals the total of all sides
= 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3
= 52 cm
2. A rectangular box with sides measuring 40 by 10 centimeters has tape around the lid. What is the necessary length of the tape?
2. A rectangular box with sides measuring 40 by 10 centimeters has tape around the lid. What is the necessary length of the tape?
Explanation:
Required tape length equals the rectangle's perimeter
(Length + Breadth) = 2
= 2 (40 + 10)
= 2 (50)
= 100 cm
The amount of tape needed is 100 cm.
3. The size of a table surface is 2 m 25 cm by 1 m 50 cm. What is the size of the tabletop's perimeter?
3. The size of a table surface is 2 m 25 cm by 1 m 50 cm. What is the size of the tabletop's perimeter?
Explanation:
Tabletop length is 2 m 25 cm, or 2.25 m.
Tabletop width is 1 m 50 cm, or 1.50 m.
Tabletop perimeter = 2 (Length + Breadth).
= 2 (2.25 + 1.50)
= 2 (3.75)
= 2 × 3.75
= 7.5 m
The top of the table measures 7.5 meters around.
4. How long of a wooden strip is needed to frame a picture with dimensions of 32 centimeters in length and 21 cm in width?
4. How long of a wooden strip is needed to frame a picture with dimensions of 32 centimeters in length and 21 cm in width?
Explanation:
The required wooden strip's length is equal to the picture's perimeter.
(Length + Breadth) = 2
= 2 (32 + 21)
= 2 (53)
= 2 × 53
= 106 cm
The wooden strip must be 106 centimeters in length.
5. A rectangle of ground has the dimensions 0.7 km by 0.5 km. Four layers of wires are to be used to fence off each side. What is the required cable length?
5. A rectangle of ground has the dimensions 0.7 km by 0.5 km. Four layers of wires are to be used to fence off each side. What is the required cable length?
Explanation:
The field's perimeter is equal to 2 (Length + Breadth).
= 2 (0.7 + 0.5)
= 2 (1.2)
= 2 × 1.2
= 2.4 km
Four rows of fencing are required on each side, or 4 2.4.
= 9.6 km
The entire needed wire length is 9.6 kilometers.
6. Determine each of the following forms' perimeters:
(a) A triangle with edges of 3, 4, and 5 centimeters
(b) A 9 cm-long equilateral triangular
(c) An isosceles triangle with a third side that is 6 cm long and equal edges that are each 8 cm long.
6. Determine each of the following forms' perimeters:
(a) A triangle with edges of 3, 4, and 5 centimeters
(b) A 9 cm-long equilateral triangular
(c) An isosceles triangle with a third side that is 6 cm long and equal edges that are each 8 cm long.
Explanation:
Triangle's perimeter (a) equals 3 + 4 + 5
= 12 cm
(b) An equilateral triangle's circumference is equal to three sides.
= 3 × 9
= 27 cm
(c) Isosceles triangular perimeter is equal to 8 + 8 + 6.
= 22 cm
7. Calculate the area of a triangle whose edges are 10 cm, 14 cm, and 15 cm long.
7. Calculate the area of a triangle whose edges are 10 cm, 14 cm, and 15 cm long.
Explanation:
Triangle's perimeter equals 10 + 14 + 15.
= 39 cm
The triangle's circumference is 39 cm.
8. Calculate the size of a standard hexagon whose sides are each 8 metres long.
8. Calculate the size of a standard hexagon whose sides are each 8 metres long.
Explanation:
Hexagonal perimeter equals 6 x 8
= 48 m
The standard hexagon's perimeter is 48 metres.
9. Locate the square's edge whose length is 20 metres.
9. Locate the square's edge whose length is 20 metres.
Explanation:
Square perimeter equals four sides.
20 = 4 × side
Side = 20 / 4
Side = 5 m
The square's side measures 5 metres.
10. A standard pentagon has a perimeter of 100 centimetres. How long is each edge of it?
10. A standard pentagon has a perimeter of 100 centimetres. How long is each edge of it?
Explanation:
The regular pentagon's perimeter is equal to 100 cm.
5 sides equal 100 cm
Side = 100 / 5
20 cm per side
The pentagon's side measures 20 cm.
11. The length of a rope is 30 cm. How long will each half be if the string is used to create:
(A) a rectangle?
(B) a triangular with equal sides?
is (c) a typical hexagon?
11. The length of a rope is 30 cm. How long will each half be if the string is used to create:
(A) a rectangle?
(B) a triangular with equal sides?
is (c) a typical hexagon?
Explanation:
(a) The square's perimeter is 30 cm.
4 × side = 30
Side = 30 / 4
Side: 7.50 cm
(b) The equilateral triangle's perimeter is 30 cm.
3 × side = 30
Side = 30 / 3
Aspect = 10 cm
(c) A normal hexagon's circumference is 30 cm.
6 × side = 30
Side = 30 / 6
Aspect = 5 cm
12. A triangle has two sides that are 12 centimetres and 14 cm long. The triangle has a 36 centimetre perimeter. What's the third part of it?
12. A triangle has two sides that are 12 centimetres and 14 cm long. The triangle has a 36 centimetre perimeter. What's the third part of it?
Explanation:
Make the third side x cm.
triangle's circumference is 36 cm.
12 + 14 + x = 36
26 + x = 36
x = 36 – 26
x = 10 cm
Third side measures 10 cm.
13. Calculate the price of enclosing a square park with a side of 250 metres at a cost of $20 per metre.
13. Calculate the price of enclosing a square park with a side of 250 metres at a cost of $20 per metre.
Explanation:
250 m is the square's side.
Square perimeter equals four sides.
= 4 × 250
= 1000 m
Fencing costs $20 per m.
1000 metres of fencing will cost $20,000.
= ₹ 20,000
The square park's fencing will cost $20,000 to install.
14. Calculate the price of fencing a rectangular park with dimensions of 175 centimetres in length and 125 m in width at a cost of 12 cents per metre.
14. Calculate the price of fencing a rectangular park with dimensions of 175 centimetres in length and 125 m in width at a cost of 12 cents per metre.
Explanation:
175 cm in length
Depth = 125 metres
Park's rectangular perimeter is equal to 2 (Length + Breadth).
= 2 (175 + 125)
= 2 (300)
= 2 × 300
= 600 m
Fencing costs equal 12 x 600.
= 7200
Fencing will set you back $7,200.
15. Sweety circles a 75-meter square field. The park Bulbul circles has a length of 60 metres and a width of 45 metres. Who travels a shorter distance?
15. Sweety circles a 75-meter square field. The park Bulbul circles has a length of 60 metres and a width of 45 metres. Who travels a shorter distance?
Explanation:
Square perimeter equals four sides.
= 4 × 75
= 300 m
300 metres are travelled by Sweety.
The rectangular park's perimeter is equal to 2 (Length + Breadth).
= 2 (60 + 45)
= 2 (105)
= 2 × 105
= 210 m
∴ Bulbul covers a distance of 210 m.
As a result, Bulbul travels shorter distances than Sweety.
16. What is each of the following symbols' perimeters? What can you deduce from the responses?
16. What is each of the following symbols' perimeters? What can you deduce from the responses?
Explanation:
(a) A square's perimeter equals four sides
= 4 × 25
= 100 cm
(b) The rectangle's perimeter is 2 (40 + 10).
= 2 × 50
= 100 cm
(c) A rectangle's perimeter equals two (length plus breadth).
= 2 (30 + 20)
= 2 (50)
= 2 × 50
= 100 cm
(d) Triangle perimeter equals 30 + 30 + 40
= 100 cm
Each figure's circumference is the same.
17. Avneet purchases 9 square paving stones with a side measurement of 1.2 metres. He arranges them into a square shape.
(A) What is the arrangement's circumference (fig. 10.7(i))?
(b) Shari disapproves of his plan. She convinces him to arrange them in a cross shape. What is the size of her arrangement's circumference (see Fig. 10.7 (ii))?
Which has a larger circumference (c)?
(d) Avneet ponders whether there is a method to obtain a perimeter that is even larger. Can you figure out how to do this? (The paving slabs must meet along complete edges, i.e. they cannot be broken.)
17. Avneet purchases 9 square paving stones with a side measurement of 1.2 metres. He arranges them into a square shape.
(A) What is the arrangement's circumference (fig. 10.7(i))?
(b) Shari disapproves of his plan. She convinces him to arrange them in a cross shape. What is the size of her arrangement's circumference (see Fig. 10.7 (ii))?
Which has a larger circumference (c)?
(d) Avneet ponders whether there is a method to obtain a perimeter that is even larger. Can you figure out how to do this? (The paving slabs must meet along complete edges, i.e. they cannot be broken.)
Explanation:
(a) Square sides equal three sides.
= 3 × 1 / 2
= 3 / 2 m
Square perimeter is equal to 4 3 / 2.
= 2 × 3
= 6 m
(b) Perimeter = 0.5 plus 1 plus 1 plus 0.5 plus 1 plus 1 plus 0.5 plus 1 plus 1
= 10 m
(c) The cross-shaped configuration has a larger perimeter.
(d) It is impossible to calculate perimeters bigger than 10 metres.
Also Read: Chapter 11: Algebra
