FRANK Solutions for Class 9 Maths Chapter 24 - Perimeter and Area

Chapter 24 - Perimeter and Area Exercise Ex. 24.1

Question 1

Find the area of a triangle whose base is 3.8 cm and height is 2.8 cm.

Solution 1

Question 2

Find the area of the shaded region in the figure as shown, in which DPQS is an equilateral triangle and ∠PQR = 90°.

Solution 2

Question 3

The area of an equilateral triangle is numerically equal to its perimeter. Find the length of its sides, correct two decimal places.

Solution 3

Question 4

In a right-angled triangle PQR right-angled at Q, QR = x cm, PQ = (x + 7) cm and area = 30 cm². Find the sides of the triangle.

Solution 4

Question 5

In a right-angled triangle ABC, if ∠B = 90°, AB - BC = 2 cm; AC - BC = 4 and its perimeter is 24 cm, find the area of the triangle.

Solution 5

Question 6

Find the area of a triangle whose sides are 27 cm, 45 cm and 36 cm.

Solution 6

Question 7

Find the area of an isosceles triangle ABC in which AB = AC = 6 cm, ∠A = 90°. Also, find the length of perpendicular from A to BC.

Solution 7

 

Question 8

Find the area of an equilateral triangle of side 20 cm.

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Chapter 24 - Perimeter and Area Exercise Ex. 24.2

Question 1

The side of a square is of length 20 mm. Find its perimeter in cm.

Solution 1

Question 2

In a rectangle ABCD, AB = 7 cm and AD = 25 cm. Find the height of a triangle whose base is AB and whose area is two times the area of the rectangle ABCD.

Solution 2

Question 3

Two adjacent sides of a parallelogram are 34 cm and 20 cm. If one of its diagonal is 42 cm, find:

a. area of the parallelogram.

b. distance between its shorter sides

Solution 3

Question 4

A rectangular floor 45 in long and 12 m broad is to be paved exactly with square tiles, of side 60 cm. Find the total number of tiles required to pave it.

If a carpet is laid on the floor such as a space of 50 cm exists between its edges and the edges of the floor, find what fraction of the floor is uncovered.

Solution 4

Question 5

The area of a square is 36 cm². How long are its sides?

Solution 5

Question 6

Find the perimeter and area of a square whose diagonal is 5cm. Give your answer correct to two decimal places if = 1.414.

Solution 6

Question 7

The sides of a rectangle are 5 cm and 3 cm respectively. Find its area in mm².

Solution 7

Question 8

The area of a rhombus is 234 cm². If its one diagonal is 18 cm, find the lengths of its side and the other diagonal. Also, find perimeter of the rhombus.

Solution 8

Question 9

The floor of a room is of size 6 m x 5 m. Find the cost of covering the floor of the room with 50 cm wide carpet at the rate of Rs.24.50 per metre. Also, find the cost of carpeting the same hall if the carpet, 60 cm, wide, is at the rate of Rs.26 per metre.

Solution 9

Question 10

A footpath of uniform width runs all around the inside of a rectangular garden of 40 m x 30 m. If the path occupies 136 m², find the width of the path.

Solution 10

Question 11

Find the area and perimeter of the given figure.

Solution 11

Question 12

How many tiles, each of area 625 cm², will be needed to pave a footpath which is 1 m wide and surrounds a grass plot of size 38 m x 14 m?

Solution 12

Question 13

 

Solution 13

Question 14

A wire when bent in the form of a square encloses an area of 16 cm². Find the area enclosed by it when the same wire is bent in the form of

a. a rectangle whose sides are in the ratio of 1 : 3.

b. an equilateral triangle

Solution 14

Question 15

Find the shaded area in the given figure.

Solution 15

Question 16

Find the area of each of the following figure:

Solution 16

Question 17

Find the area of each of the following figure:

 

Solution 17

Question 18

Find the area of each of the following figure:

Solution 18

Question 19

Find the area of each of the following figure:

Solution 19

Question 20

Find the area of quadrilateral, whose diagonals of lengths 18 cm and 13 cm intersect each other at right angle.

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36

Solution 36

Question 37

Solution 37

Question 38

Solution 38

Question 39

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

Solution 46

Question 47

Solution 47

Question 48

Solution 48

Question 49

Solution 49

Question 50

Solution 50

Chapter 24 - Perimeter and Area Exercise Ex. 24.3

Question 1

The diameter of two circles are 28 cm and 24 cm. Find the circumference of the circle having its area equal to sum of the areas of the two circles.

Solution 1

Question 2

The radii of two circles are in the ratio 5 : 8. If the difference between their areas is 156p cm², find the area of the bigger circle.

Solution 2

Question 3

The diameters of three wheels are in the ratio 2 : 4 : 8. If the sum of the circumferences of these circles be 132 cm, find the difference between the areas of the largest and the smallest of these wheels.

Solution 3

Question 4

The area of the circular ring enclosed between two concentric circles is 88 cm². Find the radii of the two circles, if their difference is 1 cm.

Solution 4

Question 5

The sum of the radii of two circles is 10.5 cm and the difference of their circumferences is 13.2 cm. Find the radii of the two circles.

Solution 5

Question 6

A square is inscribed in a circle of radius 6 cm. Find the area of the square. Give your answer correct to two decimal places if= 1.414.

Solution 6

Question 7

The cost of fencing a circular field at the rate of Rs.250 per metre is Rs.55000. The field is to be ploughing at the rate of Rs.15 per m². Find the cost of ploughing the field.

Solution 7

Question 8

The circumference of a circle exceeds its diameter by 450 cm. Find the area of the circle.

Solution 8

Question 9

The circumference of a circle is numerically equal to its area. Find the area and circumference of the circle.

Solution 9

Question 10

The sum of the circumference and diameter of a circle is 176 cm. Find the area of the circle.

Solution 10

Question 11

Find the radius and area of the circle which has circumference equal to the sum of circumferences of the two circles of radii 3 cm and 4 cm respectively.

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36

Solution 36