Question 1

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

Accepted Answer

Area of the park = (60 x 40) = 2400 m 2 Area of the lawn = 2109 m 2 Area of the crossroads = (2400 - 2109) = 291 m 2 Let the width of the road be x metres. Then, 60 x + 40 x - X 2 = 291 x 2 - 100 x + 291 = 0 (x - 97)(x - 3) = 0 x = 3.

Question 2

The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. 24.68 per hectare be Rs. 333.18, find its base and height.

Accepted Answer

Area of the field = Total cost/rate = (333.18/25.6) = 13.5 hectares 13 . 5 * 10000 m 2 = 135000 m 2 Let altitude = x metres and base = 3x metres. Then, 1 2 * 3 x * x = 135000 ⇒ x 2 = 90000 ⇒ x = 300 Base = 900 m and Altitude = 300 m.

Question 3

A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 75 paise per sq m is

Accepted Answer

Area to be plastered = 2 l + b × h + l × b = 2 25 + 12 × 6 + 25 × 12 = 744 s q . m Cost of plastering = 744 × 75 100 = R s . 558

Question 4

The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq.cm. Find its height?

Accepted Answer

Let height =x Then, base =2x 2x * x = 72 =>x=6

Question 5

The ratios of areas of two squares, one having its diagonal double than the other is

Accepted Answer

ratio = 1 / 2 × 2 d 2 1 2 d 2 = 4 : 1

Question 6

A room 5m 55cm long and 3m 74cm broad is to be paved with square tiles.Find the least number of square tiles required to cover the floor?

Accepted Answer

Area of the room=(544 * 374) size of largest square tile= H.C.F of 544 & 374 = 34 cm Area of 1 tile = (34 x 34) c m 2 Number of tiles required== [(544 x 374) / (34 x 34)] = 176

Question 7

Find the area of a right-angled triangle whose base is 12 cm and hypotenuse is 13cm.

Accepted Answer

Height of the triangle = 13 2 - 12 2 = 25 = 5 cm. Its area = 1 2 * b a s e * h e i g h t = 1 2 * 12 * 5 = 30 c m 2 .

Question 8

The length of a rectangle is twice its breadth if its length is decreased by 5cm and breadth is increased by 5cm, the area of the rectangle is increased by 75 sq cm. Find the length of the rectangle.

Accepted Answer

let length = 2x and breadth = x then (2x-5) (x+5) = (2x * x)+75 5x-25 = 75 => x=20 length of the rectangle = 40 cm

Question 9

The diameter of the driving wheel of a bus is 140 cm. How many revolution, per minute must the wheel make in order to keep a speed of 66 kmph ?

Accepted Answer

Circumference = No.of revolutions * Distance covered Distance to be covered in 1 min. = (66 X1000)/60 m = 1100 m. Circumference of the wheel = 2 x (22/7) x 0.70 m = 4.4 m. Number of revolutions per min. =(1100/4.4) = 250.

Question 10

A room of 5m 44cm long and 3m 74cm broad is to be paved with squre tiles. Find the least number of squre tiles required to cover the floor.

Accepted Answer

area of the room = 544 x 374 sq.cm size of largest square tile = H.C.F of 544cm and 374 cm= 34 cm area of 1 tile = 34x34 sq cm no. of tiles required = (544 x 374) / (34 x 34) = 176

Question 11

Find the area of a triangle whose sides measure 13 cm, 14 cm and 15 cm.

Accepted Answer

Let a = 13, b = 14 and c = 15. Then, s = 1 2 a + b + c =21 (s- a) = 8, (s - b) = 7 and (s - c) = 6. Area = s s - a s - b s - c = 21 × 8 × 7 × 6 = 84 sq.cm

Question 12

The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

Accepted Answer

Let original length = x and original breadth = y. Original area = xy. New length = x/2 and New breadth=3y New area = 3 2 x y Therefore, Increase in area = New area-original area = 3 2 x y - x y = 1 2 x y Therefore, Increase % = i n c r e a s e i n a r e a o r i g i n a l a r e a * 100 = 1 2 x y x y * 100 = 50 %

Question 13

The length of a class room floor exceeds its breadth by 25 m. The area of the floor remains unchanged when the length is decreased by 10 m but the breadth is increased by 8 m. The area of the floor is

Accepted Answer

Let the breadth of floor be 'b' m. Then, length of the floor is 'l = (b + 25)' Area of the rectangular floor = l x b = (b + 25) × b According to the question, (b + 15) (b + 8) = (b + 25) × b b 2 + 8 b + 15 b + 120 = b 2 + 25 b 2b = 120 b = 60 m. l = b + 25 = 60 + 25 = 85 m. Area of the floor = 85 × 60 = 5100 sq.m.

Question 14

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

Accepted Answer

100 cm is read as 102 cm. A1 = (100*100)Sq.cm A2 = (102*102)Sq.cm (A2 - A1) = 102 2 - 100 2 = (102 + 100) x (102 - 100) = 404 sq.cm.

Question 15

The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

Accepted Answer

2 l + b b = 5 1 => 2l + 2b = 5b => 3b = 2l b=(2/3)l Then, Area = 216 cm2 => l x b = 216 => l x (2/3)l =216 l = 18 cm.

Question 16

Three circles of radius 3.5cm are placed in such a way that each circle touches the other two. The area of the portion enclosed by the circles is

Accepted Answer

required area = (area of an equilateral triangle of side 7 cm)- (3 * area of sector with Ã = 60 degrees and r = 3.5cm) 3 4 * 7 * 7 - 3 * 22 7 * 3 . 5 * 3 . 5 * 60 360 sq cm = 3 4 * 49 - 11 * 0 . 5 * 3 . 5 sq cm = 1.967 sq cm

Question 17

The dimensions of a room are 10m x 7m x 5m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1m x 3m. One window is of size 2m x 1.5m and the other 2 windows are of size 1m x 1.5m. The cost of painting the walls at Rs. 3 …

Accepted Answer

Area of 4 walls = 2(l+b)h =2(10+7) x 5 = 170 sq m Area of 2 doors and 3 windows = 2(1x3)+(2x1.5)+2(1x1.5) = 12 sq m area to be planted = 170 -12 = 158 sq m Cost of painting = Rs. 158 x 3 = Rs. 474

Question 18

Area of a square and a rectangle are equal. If side of the square is 40 cm and length of the rectangle is 64 cm, what is the perimeter of the rectangle ?

Accepted Answer

Area of square = 40 x 40 = 1600 sq.cm Given that the areas of Square and Rectangle are equal => Area of rectangle = 1600 Sq.cm We know that, Area of rectangle = L x B Given L = 64 cm Breadth of rectangle = 1600/64 = 25 cm Perimeter of the rectangle = 2(L + B) = 2(64+25) = 178 cm.

Question 19

The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, find its height

Accepted Answer

Let the height of the parallelogram be x. cm. Then, base = (2x) cm. 2 x × x = 72 = > 2 x 2 = 72 = > x = 6

Area Questions