Question 1

The perimeter of a square is equal to twice the perimeter of a rectangle of length 8cm and breadth 7cm. What is the circumference of a semicircle whose diameter is equal to the side of the square ?

Accepted Answer

We know that perimeter of rectangle = 2(l+b) = 2(8+7)= 30cm Given perimeter of square is twice the perimeter of rectangle = 2(30) = 60cm Therefore, side of the square is = 1/4 x 60 = 15cm Circumference of the required semicircle = πr + 2 r = 22 7 × 15 2 + 2 × 15 2 = 23.57 + 15 = 38.57cm.

Question 2

If a 36 cm thread is used to wrap a book, lengthwise twice and breadth wise once, what is the size of the book ?

Accepted Answer

Length of the thread is 36 cms. length wise twice breath wise once then totally thrice. so 36/3 = 12. so length is 12 x 2 = 24 cms breath is 12 cms Area of the book = length x breath = 24 x 12 = 288 sq.cm

Question 3

A man walking at the speed of 4 kmph crosses a square field diagonally in 3 meters.The area of the field is

Accepted Answer

speed of the man = 4 x (5/18) m/sec = 10/9 m/sec time taken = 3 x 60 sec = 180 sec length of diagonal = speed x time = (10/9) x 180 = 200m Area of the field = (1/2) x (dioagonal)² = (1/2) x 200 x 200 sq.m = 20000sq.m

Question 4

If the ratio of two squares is 225:256,then the ratio of the perimeters is

Accepted Answer

a 2 b 2 = 225 / 256

Question 5

The area of a square is 1024 sq.cm. What is the ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is 12 cm less than the side of this square ?

Accepted Answer

Area of a square SxS = 1024 => S = 32 cm Length of the rectangle = 32x2 cm = 64 cm Breadth of the rectangle = 32 - 12 = 20 cm Required ratio = 64 : 20 = 16 : 5

Question 6

A rectangular grassy plot 120 m. by 60 m has a gravel path 1.5 m wide all round it on the inside. Find the cost of gravelling the path at 65 paise per sq. metre ?

Accepted Answer

area of the plot = 120m x 60m = 7200 sq.m area of plot excluding gravel = 117m x 57m = 6669 sq.m area of gravel = 7200 sq.m - 6669 sq.m = 531 sq.m cost of building it = 531 sq.m x 65 ps = 34515 ps In Rs. = 34515/100 = Rs. 345.15.

Question 7

The wheel of a motorcycle 70cm in diameter makes 40 revolutions in every 10sec.What is the speed of motorcycle n km/hr?

Accepted Answer

In this type of question, we will first calculate the distance covered in given time. Distance covered will be : Number of revolutions x Circumference So we will be having distance and time, from which we can calculate the speed. Radius of wheel = 70 / 2 = 35 cm Distance covered in 40 revolutions will be 40 * c i r c u m f e r e n e = 40 * 2 πr = 40 * 2 * 22 7 * 35 = 8800 cm = 88 m Distance covered in 1 sec = 88 10 = 8 . 8 m / s = 8 . 8 * 18 5 k m / h r = 31 . 68 k m / h r

Question 8

The base of a triangle of 15cm and height is 12cm. The height of another triangle of double the area having the base 20cm is

Accepted Answer

a = 1 2 × 15 × 12 = 90 sq.cm b = 2a = 1 2 × 20 × h h= 18cm

Question 9

The inner circumference of a circular race track, 14m wide is 440m. Find the radius of the outer circle.

Accepted Answer

let inner radius be r meters. 2 πr = 440 ⇒ r = 440 × 7 44 = 70 m radius of outer circle = 70 + 14 m Therefore, Radius of outer circle = 70 + 14 = 84m

Question 10

If 4 circles of equal radius are drawn with vertices of a square as the centre , the side of the square being 7 cm, find the area of the circles outside the square ?

Accepted Answer

Because each vertice of the square is the center of a circle (1/4) part of the total area of each circle inside of the square. (3/4) part of the total area of each circle outside of the square. Thus total area outside the square is 4 3 4 × 22 7 × 3 . 5 × 3 . 5 = 115.3955 sq cm.

Question 11

A rectangular lawn of dimensions 80 m x 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m ?

Accepted Answer

Area = (l + b – d) d = (80 + 60 – 10)10 => 1300 sq.mts => 1300 x 3 = Rs.3900

Question 12

The perimeter of a rectangle whose length is 6 metre more than its breadth is 84 metre. What is the area of the triangle whose base is equal to the diagonal of the rectangle and height is equal to the length of the rectangle?

Accepted Answer

Let the breadth of rectangle be x m. Then, the length of rectangle = (x+ 6) m Perimeter of rectangle = 2 (x+x+ 6) m Therefore, 2 (x+x+ 6) = 84 m 4x+ 12 = 84 4x= 84 –12 4x = 72/4 = 18 Therefore, length of rectangle = 18 + 6 = 24 m = height of triangle Diagonal of rectangle = √(324+576) = 30 m = base of triangle Therefore, are of triangle =1/2× base × height =1/2× 24 × 30 = 360 sq. m

Question 13

The length and breadth of a rectangle is in the ratio of 3 : 1. If its perimeter is 96 m, then what is the length of the rectangle?

Accepted Answer

Let the length of the rectangle be 3x and breadth be 1x Given, perimeter = 96 m 2(l + b) = 96 (or) l + b = 48 (or) 3x + 1x = 48 (or) x = 12 m Now, Length of the rectangle = 12 x 3 = 36 m

Question 14

The hypotenuse of a right-angled triangle 10 cm and its area is 24 cm^2. If the shorts side is halved and the longer side is double, the new hypotenuse becomes

Accepted Answer

Hypotenuse = 10cm Let the other 2 perpendicular sides be a and b Area ½ a*b = 24 So a*b = 48 cm^2 Also using Pythagoras

Area Questions