Question 1

If the sides of a rectangle are increased by 10% find the percentage increased in its diagonals.

Accepted Answer

According to the formula, ∵ Percentage increase in sides = 10% ∴ Percentage increase diagonals = 10%

Question 2

What is the diameter of the circle having 3 cm radius?

Accepted Answer

Radius = Diameter/2 ∴ Diameter = 2 x Radius = 2 x 3 = 6 cm

Question 3

The radius of a circular field is 25 m. Find the area of the field.

Accepted Answer

Required area = πr2 = π x 25 x 25 = 625π sq m.

Question 4

The length and breadth of a rectangular piece of land are in the ratio of 5:3, the owner spent Rs.3000 for surrounding it from all the sides at Rs.7.50 per meter. The different between its length and breadth is?

Accepted Answer

Let Length = 5y meters and breadth = 3y meters. Then, perimeter = 2 x (5y + 3y ) m = 16y meters ...(i) But perimeter = Total Cost / Rate = 3000 / 7.50 m = 400 m ...(ii) from eqs. (i) and (ii) 16y = 400 ⇒ y = 25 ∴ Length - Breadth = (5 x 25 - 3 x 25 ) m = 2 x 25 m = 50 m

Question 5

One side of a rectangular field is 4 meter and its diagonal is 5 meter. The area of the field is?

Accepted Answer

Other side = √5 2 - 42 = √ 9 =3 m So The area of the rectangular field = 4 x 3 = 12 m2

Question 6

If the base of a rectangular is increased by 10% and the area is unchanged , then the corresponding altitude must to be decreased by?

Accepted Answer

Let base = b and altitude = h Then, Area = b x h But New base = 110b / 100 = 11b / 10 Let New altitude = H Then, Decrese = (h - 10h /11 ) = h / 11 ∴ Required decrease per cent = (h/11) x (1 / h ) x 100 % = 91/11 %

Question 7

The length of hall is (4/3) times its breadth. If the area of hall be 300 square meters, the difference between the length and the breadth is?

Accepted Answer

Let breadth = b meters. Then, length = 4b/3 meters. ∵ b x 4b/3 = 300 ⇒ b2 = 300 x 3/4 ⇒ b2 = 225 ∴ b = 15 Hence, required difference = [(Length) - (Breadth) ] = 4b/3 - b = b/3 = 15/3 m = 5 m

Question 8

The cost of cultivating a square field at the rate of Rs. 160 per hectare is Rs. 1440. the cost of putting a fence around it at 75 paisa per meter is?

Accepted Answer

Area = 1440 / 160 hectares = 9 hectares = 90000 m2 ∴ One side = √90000 m = 300 m So perimeter = 4 x 300 m = 1200 m ∴ Cost of fencing = Rs (1200 x 75) / 100 = Rs. 900

Question 9

A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?

Accepted Answer

Let breadth = b meters. then, length = 3b/2 meters ∴ b x 3b/2 = 2/3 X 10000 ⇒ b2 = (4 x 10000)/9 ⇒ b = ( 2 X 100)/3 m ∴ Length = (3/2) x (2/3) x 100 m = 100 m

Question 10

The ratio between the length and breadth of a rectangular field is 5:4. If the breadth is 20 meters less than the length, the perimeters of the field is?

Accepted Answer

Let length of rectangular field = 5y, so width = 4y. From question 5y - 4y = 20m ⇒ x = 20m ∴ Length = (5 x 20)m = 100 m Breadth = (4 x 20) m = 80 m ∴ Perimeter = 2 (100 + 80 ) m = 360 m

Question 11

The area of a rectangle, 144 m long is the same as that of a square having a side 84 m long. The width of the rectangle is?

Accepted Answer

Area of the square = (84 + 84) m2 Area of the rectangle = (144 x width) m2 From question both area would be same, ∴ Width = (84 x 84) / 144 m = 49 m

Question 12

The length of a plot is four times its breath. A playground measuring 1200 square meters occupies one third of the total area of a plot . what is the length of the plot in meters?

Accepted Answer

Area of the plot = (3 x 1200) m2 = 3600 m2 Let breadth = y meters Then Length = 4y meters, Now area = 4y x y = 3600 m2 ⇒ y2 = 900 m2 ⇒ y = 30 m ∴ Length of plot = 4y m = (4 x 30) m =120 m

Question 13

The cost of papering the four walls of a room is Rs. 48. Each one of length, breadth and height of another room is double that of this room.The cost of papering the walls of the new room is?

Accepted Answer

Let the length, breadth and height of the room be l, b and h respectively As per question Cost of 2(l + b) x h = Rs. 48 ∴ Required cost = cost of 2 (2l + 2b) x 2h = cost of 4 [2(l + b) x h ] = 4 x Rs. 48 = Rs. 192

Question 14

Area of a four walls a room is 168 Sq. meters . The breadth and height of a room are 8 meters and 6 meters respectively . The length of the room is?

Accepted Answer

Area of a four walls = 2(l + 8) x 6 = 168m2 ⇒ (l + 8) = 14 ∴ l = 14-8 = 6 meters

Question 15

Area of a four wall of a room is 77 square meters . the length and breadth of room are 7.5 meters and 3.5 meters respectively . the height of the room is?

Accepted Answer

Area of four walls = 2 x (l + b ) x h ⇒ 2 x (7.5 + 3.5 ) x h = 77 m2 ⇒ h = 77 / (2 x 11) = 7/2 ∴ h = 3.5 meters

Question 16

A rectangle has 15 cm as its length and 150 cm 2 as its area .Its area is increased to 1 1 / 3 times the original area by increasing only its length . Its new perimeter is?

Accepted Answer

Breadth of the rectangle = (150/15) cm = 10 cm New area = (4/3 x 150) cm2 = 200 cm2 New length = 200/10 cm =20 cm New perimeters = 2(20 + 10) cm = 60 cm

Question 17

The length of a rectangle room is 4 meters . if it can be partitioned into two equal square rooms . what is the length of each partition in meters?

Accepted Answer

Let the width of the room be x members Then, its area = (4x) m2 Area of each new square room = (2x)m2 Let the side of each new room = y meters Then, y2 = 2x Clearly, 2x is a complete square when x=2 ∴ y2 = 4 ⇒ y = 2 m .

Question 18

The length and breadth of a square are increased by 40% and 30% respectively. The area of a resulting rectangle exceeds the area of the square by?

Accepted Answer

Let the side of the square = 100 m So area of square = 100 x 100 = 10000. New length = 140 m, New breadth = 130 m Increase in area = [(140 x 130) - (100 x 100)] m2 = 8200 m2 ∴ Required increase percent = (8200/ 10000) x 100 % = 82%

Question 19

A hall 20 m long and 15 m broad is surrounded by a verandah of uniform width of 2.5 m. the cost of flooring the verandah at the rate of 3.50 per sq. meter is?

Accepted Answer

Area of verandah = [(25 x 20) -(20 x 15)] m2 = 200 m2 ∴ Cost of flooring = Rs. (200 x 3.50) = Rs. 700

Question 20

Of the square fields the area of the one is 1 hectare, while the another one is broader by 1% the difference is area is?

Accepted Answer

Area of the square field = 1 hectare = 10000 m2 Side of the square = √ 10000 m = 100 m Side of another square field = 100 + 1 = 101 m ∴ Required difference of area = [(101)2 - (100)2] m2 =[(101 + 100 ) (101 - 100) ] m2 = 201 m2

Area Questions