## 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