Question 1

The base of a parallelogram is twice its height. If the area of the parallelogram is 338 sq.cm. Find its height?

Accepted Answer

Let height =x Then, base =2x 2x * x = 338 =>x=13

Question 2

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 3

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 4

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

Accepted Answer

Let the breadth of the given rectangle be x then length is 2x. thus area of the given rect is 2 x 2 after dec 5cm from length and inc 5cm breadth , new lenght becomes 2x-5 and breadth is x+5.thus new area =(2x-5)(x+5)= 2 x 2 + 5 x - 25 since new area is 75 units greater than original area thus 2 x 2 + 75 = 2 x + 5 x - 25 5x=75+25 5x=100 therefore x=20 hence length of the rectangle is 40 cm.

Question 5

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 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

The area of a square is equal to the area of a rectangle. The length of the rectangle is 5 cm more than a side of the square and its breadth is 3 cm less than the side of the square. What is the perimeter of the rectangle ?

Accepted Answer

Let the side of the square be 's' cm length of rectangle = (s+5) cm breadth of rectangle = (s-3)cm (s+5) (s-3) = s 2 - 5s - 3s - 15 = s 2 2s = 15 Perimeter of rectangle = 2(L+B) = 2(s+5 + s–3) = 2(2s + 2) = 2(15 + 2) = 34 cm

Question 15

The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? Question : What is the height of a right-angled triangle ? Statements : A. T…

Accepted Answer

From statement (A), 20b = (1/2) × b × h h = 40 cm.

Question 16

A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq.m is Rs. 270 and the cost of papering the four walls at Rs. 10 per sq.m is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.

Accepted Answer

Let breadth = x metres, length = 3x metres, height = H metres. Area of the floor=(Total cost of carpeting)/(Rate) = (270/5) sq.m = 54 sq.m x × 3 x 2 = 54 ⇒ x 2 = 54 × 2 ⇒ x = 6 So, breadth = 6 m and length = 3 6 2 = 9 m. Now, papered area = (1720/10) = 172 sq.m Area of 1 door and 2 windows = 8 sq.m Total area of 4 walls = (172 + 8) sq.m = 180 sq.m 2 × 9 + 6 H = 180 ⇒ H = 6

Question 17

A man runs round a circular field of radius 50m at the speed of 12 km/hr. What is the time taken by the man to take twenty rounds of the field?

Accepted Answer

speed = 12 km/h = 12 × 5 18 = 10 3 m / s distance covered = 20 × 2 × 22 7 × 50 = 44000 7 m time taken = distance /speed = 44000 7 × 3 10 s e c = 4400 × 3 7 × 1 60 m i n = 220 7 m i n

Question 18

A rectangular lawn 55m by 35m has two roads each 4m wide running in the middle of it. One parallel to the length and the other parallel to breadth. The cost of graveling the roads at 75 paise per sq meter is

Accepted Answer

area of cross roads = (55 x 4) + (35 x 4)- (4 x 4) = 344sq m cost of graveling = 344 x (75/100) = Rs. 258

Question 19

The cost of fencing a square field @ Rs. 20 per metre is Rs.10.080.How much will it cost to lay a three meter wide pavement along the fencing inside the field @ Rs. 50 per sq m

Accepted Answer

perimeter = total cost / cost per m = 10080 /20 = 504m side of the square = 504/4 = 126m breadth of the pavement = 3m side of inner square = 126 - 6 = 120m area of the pavement = (126 x126) - (120 x 120) = 246 x 6 sq m cost of pavement = 246*6*50 = Rs. 73800

Area Questions