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# Exercise 3.1

6th Maths : Term 3 Unit 3 : Perimeter and Area : Exercise 3.1 : Text Book Back Exercises Questions with Answers, Solution

Exercise 3.1

1. The table given below contains some measures of the rectangle. Find the unknown values. i) Length of rectangle (l) = 5 cm

Perimeter P = 2 ( l + b ) units

= 2 (5 + 8) cm

= 2 × 13 cm = 26 cm

Area A = l + b sq. units

= 5 × 8 sq. cm

= 40 sq. cm

ii) Length of rectangle (l) = 13 cm

Perimeter P = 2 ( l + b ) units  = 54 cm

2 (13 + b) = 54

13 + b = 27

b = 27 – 13 = 14 cm

Area A = l × b

= 13 × 14 sq.cm

= 182 sq.cm

iii) Length of rectangle l = ?

Perimeter P = 2 ( l + b ) = 60 cm

l + b  = 30

l = 30 – 15 = 15 cm

Length l = 15 cm

Area A = l × b sq.units

= 15 × 15 = 225 sq.cm

iv) Length of rectangle l = 10 m

Area A = l × b sq. units  = 120 sq.m

10 × b = 120

b = 120/10 = 12 m

Perimeter P = 2 ( l + b ) units

= 2 ( 10 + 12) m

= 2 × 22 m = 44 m

v)  Length of rectangle l = ?

Area A = l × b sq. units  = 20 sq.feet

l × 4 = 20

l = 20/4 = 5 feet

Length l = 5 feet

Perimeter P = 2 ( l + b ) units

= 2 ( 5 + 4 ) feets

= 2 × 9 = 18 feets 2. The table given below contains some measures of the square. Find the unknown values. i) Side of square S =  6 cm

Perimeter P = 4S = 4 × 6 = 24 cm

Area A = S × S = 6 × 6 = 36 sq.cm

ii) Perimeter of square P = 4S = 100 m

S = 25 m

Area A = S × S sq.unit

= 25 × 25 = 625 sq.m

iii) Area of square A = S × S = 49 sq.feet

S × S = 7 × 7

S = 7 feet

Perimeter P = 4S = 4 × 7 = 28 feet 3. The table given below contains some measures of the right angled triangle. Find the unknown values. i) In right angled triangle,

Base b = 20 cm

Height h = 40 cm

Area A = ½ bh sq.units

= 1/2 × 20 × 40 sq.cm

Area = 400 sq.cm = 400 sq.cm

ii) In right angled triangle,

Base b = 5 feet

Height h = ?

Area A = ½ bh sq.units = 20 sq.feet

= 1/2 × 5 × h = 20

h = 20/5 × 2  = 8 feet

Height h = 8 feet

iii) In right angle triangle,

Base b = ?

Height h = 12 m

Area A = ½ bh sq.units = 24 sq.m.

= 1/2 × b × 12 = 24

b = 24 / 6 = 4 m

Base b = 4 m 4. The table given below contains some measures of the triangle. Find the unknown values. i) Measures of sides of the triangle,

a = 6 cm

b = 5 cm

c = 2 cm

Perimeter P = a + b + c units

= 6 + 5 + 2 = 13 cm

ii) Measures of sides of the triangle,

a = ?

b = 8 m

c = 3 m

Perimeter P = a + b + c units = 17 m

=  a + 8 + 3 = 17 m

= a + 11 = 17

a = 17 – 11 = 6 m

Measure of one side a = 6 m

iii) Measures of sides of the triangle,

a =11 feet

b = ?

c  = 9 feet

Perimeter P = a + b + c units = 28 feet

= 11+ b + 9 = 28

= b + 20 = 28

b = 28 − 20 = 8 feet

Measure of one side b = 8 feet. 5. Fill in the blanks.

i) 5 cm2500 mm2

ii) 26 m2260000 cm2

iii) 8 km28000000 m2

6. Find the perimeter and area of the following shapes. i)

Measure of one side S = 4 cm

Number of sides = 12

Perimeter P = 12 × S = 12 × 4 = 48 cm

Measure of one side of the square S = 4 cm

Area A = S × S = 4 × 4 = 16 Sq.cm

Number of squares = 5

Area of 5 squares = 5 × 16 = 80 sq.cm

ii)

Height of right angled triangle = 4 cm

Hypoteouse = 5 cm

Height of one triangle + Hypotenuse = (4 + 5) cm

= 9 cm

Height and Hypotenuse of 4 right angled triangles = 4 × 9 = 36 cm

Perimeter P = 36 cm

Area of one right angled triangle A = ½  bh sq.units

= 1/2  × 3 × 4 = 6 sq.cm

Area of four triangles = 4 × 6 = 24 sq.cm

Measure of one side of the middle square

S = 3 cm

Area A = S × S sq.units

= 3 × 3 = 9 sq.cm

Total Area = Area of four triangle + Area of the middle square

= (24 + 9) sq.cm = 33 sq.cm

iii)

Perimeter of the shape = (50 + 12 + 13 + 40 + 10 + 10 + 15) cm

= 150 cm

Length of rectangle l = 50 cm

Area A = l × b = 50 × 5 = 250 sq.cm

Area of triangle A = ½  bh

= 1/2  × 5 × 12 = 30 sq.cm

Area of square A = S × S = 10 × 10 = 100 sq.cm

Total area of the shape  = Area of rectangle + Area of triangle + Area of square

= (250 + 30 + 100) sq.cm

= 380 sq.cm

7. Find the perimeter and the area of the rectangle whose length is 6 m and breadth is 4 m.

Length of rectangle l = 6 m

Perimeter P = 2 (l + b) units

= 2 (6 + 4) m

= 2 × 10 = 20 m

Area A =  l × b sq.units

= 6 × 4 = 24 sq.m

8. Find the perimeter and the area of the square whose side is 8 cm.

Side of the square S = 8 cm

Perimeter P = 4 S units

= 4 × 8 = 32 cm

Area A = S × S sq.units

= 8 × 8 = 64 sq.cm

9. Find the perimeter and the area of a right angled triangle whose sides are 6 feet, 8 feet and 10 feet.

Measures of the sides of the right angled 6 feet, 8 feet and 10 feet.

Perimeter P = (6 + 8+10) feet

= 24 feet

Area A = ½  bh sq. units

= 1/2 × 6 × 8 sq.cm

= 24 sq.feet

10. Find the perimeter of

i) A scalene triangle with sides 7 m, 8 m, 10 m.

Sides of scalene triangle a = 7 m, b = 8 m and c = 10 m

Perimeter P = a + b + c units

= (7 + 8 + 10) m = 25 m

ii) An isosceles triangle with equal sides 10 cm each and third side is 7 cm.

Sides of isosceles triangle, a = 10 cm, b = 10 cm and c = 7 cm

Perimeter P = a + b + c units

= (10 + 10 + 7) cm = 27 cm

iii) An equilateral triangle with side 6 cm.

Side of equilateral triangle, a = 6 cm

Perimeter P = 3 a = 3 × 6 = 18 cm

11. The area of a rectangular shaped photo is 820 sq. cm. and its width is 20 cm. What is its length? Also find its perimeter.

Area of a rectangular shaped photo = 820 sq.cm

l × b = 820 sq.cm.

width b = 20 cm

l × 20 = 820

l = 820 / 20  = 41 cm

length l  =  41 cm

Perimeter P = 2 (l + b) units

= 2 (41+ 20) cm

= 2 × 61 = 122 cm

Perimeter P = 122 cm

12. A square park has 40 m as its perimeter. What is the length of its side? Also find its area.

Perimeter of a square park P = 4 × S = 40 m

Side S = 40 / 4  = 10 cm

Side of the square park = 10 m

Area of the square park = S × S sq.units

= 10 × 10 sq.m

= 100 sq.m

13. The scalene triangle has 40 cm as its perimeter and whose two sides are 13 cm and 15 cm, find the third side.

Perimeter of a scalene triangle = 40 cm

Measure of two sides a = 13 cm and b = 15 cm

The third side C = ?

Perimeter P = a + b + C = 40 cm

13 + 15 + C = 40

28 + C = 40

C = 40 – 28 = 12 cm

The third side = 12 cm

14. A field is in the shape of a right angled triangle whose base is 25 m and height 20 m. Find the cost of levelling the field at the rate of 45/- per sq. m2.

Base of a right angled triangle b = 25 m

Height h = 20 m

Area A = ½ bh units

= 1/2 × 25 × 20 sq.m.

= 250 sq.m.

The cost of levelling the field for l sq.m = ₹ 45

The cost of levelling the field for 250 sq.m = ₹  45 × 250

= ₹ 11250

The cost of levelling the field = ₹  11250

15. A square of side 2 cm is joined with a rectangle of length 15 cm and breadth 10 cm. Find the perimeter of the combined shape. The Perimeter of the combined shape = 2 length + 1 breadth of rectangle + 3 sides of square + 8 cm

= (2 × 15 + 10 + 3 × 2 + 8) cm

= (30 + 10 + 6 + 8) cm

= 54 cm

The perimeter of the combined shape = 54 cm

Objective Type Questions

16. The following figures are of equal area. Which figure has the least perimeter? 17. If two identical rectangles of perimeter 30 cm are joined together, then the perimeter of the new shape will be

a) equal to 60 cm

b) less than 60 cm

c) greater than 60 cm

d) equal to 45 cm

Answer: b) less than 60 cm

18. If every side of a rectangle is doubled, then its area becomes _____ times.

a) 2

b) 3

c) 4

d) 6

19. The side of a square is 10 cm. If its side is tripled, then by how many times will its perimeter increase?

a) 2 times

b) 4 times

c) 6 times

d) 3 times

20. The length and breadth of a rectangular sheet of a paper are 15 cm and 12 cm respectively. A rectangular piece is cut from one of its corners. Which of the following statement is correct for the remaining sheet?

a. Perimeter remains the same but the area changes

b. Area remains the same but the perimeter changes

c. There will be a change in both area and perimeter.

d. Both the area and perimeter remains the same.

Answer: c) There will be a change in both area and perimeter.

Exercise 3.1

1. i) 26 cm, 40 cm2 ii) 14 cm, 182 cm2 iii) 15 cm, 225 cm2 iv) 12 m, 44 cm v) 5 feet, 18 feet

2. i) 24 cm, 36 cm2 ii) 25 m, 625 cm2 iii) 7 feet, 28 feet

3. i) 400 cm2 ii) 8 feet iii) 4 m

4. i) 13 m ii) 6 m iii) 8 feet

5. i) 500 ii) 2,60,000 iii) 80,00,000

6. i) 48 cm, 80 cm2 ii) 36 cm, 49 cm2 iii) 150 cm, 380 cm2

7. 20 m, 24 m2

8. 32 cm, 64 cm2

9. 24 feet, 24 sq. feet

10. i) 25 m ii) 27 cm iii) 18 cm

11. 41 cm, 122 cm

12. 10 m, 100 m2

13. 12 cm

14. 250 m2, ₹11250/-

15. 54 cm

16. b)

17. b) less than 60 cm

18. c) 4 times

19. d) 3 times

20. c) Both the area & perimeter are changed

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6th Maths : Term 3 Unit 3 : Perimeter and Area : Exercise 3.1 | Questions with Answers, Solution | Perimeter and Area | Term 3 Chapter 3 | 6th Maths