Question 1

If the diagonals of a rhombus are 24cm and 10cm the area and the perimeter of the rhombus are respectively.

Accepted Answer

Area = 1 2 * d i a g o n a l 1 * 1 2 d i a g o n a l 2 = 1 2 * 24 * 10 sq.cm 1 2 * d a i g o n a l 1 = 1 2 * 24 = 12 c m 1 2 * d i a g o n a l 2 = 1 2 * 10 = 5 c m side of a rhombus = (12)² + (5)² = 169 => AB = 13cm

Question 2

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 3

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 4

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 5

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 6

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 7

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 8

Find the curved surface area (in cm²) of a hemisphere of diameter 28 cm

Accepted Answer

1232

Question 9

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 10

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

Question 11

What is the area (in sq cm) of a rectangle if its diagonal is 26 cm and one of its sides is 10 cm?

Accepted Answer

240

Question 12

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:3 and area of ΔABC is 100 sq cm, what is the area (in sq cm) of quadrilateral BDEC?

Accepted Answer

84

Question 13

The area of a circle is 616 sq cm, find its circumference?

Accepted Answer

88 cm

Question 14

The area of the largest sphere ( in cm2) that can be drawn inside a square of side 18 cm is

Accepted Answer

972Π

Question 15

The four sides of a quadrilateral are in the ratio of 2:3:4:5 and its perimeter is 280m. The length of the longest side is

Accepted Answer

100m

Question 16

In ΔABC, AC = BC and ∠ABC = 50°, the side BC is produced to D so that BC = CD then the value of ∠BAD is

Accepted Answer

90°

Question 17

A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

Accepted Answer

Let original length = x and original breadth = y. Decrease in area = xy - 80 100 x × 90 100 y = (7/25)xy Decrease % = (7/25)xy * (1/xy) * 100 = 28%

Question 18

A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

Accepted Answer

We have: l = 20 ft and lb = 680 sq. ft.So, b = 34 ft. Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.

Question 19

Find the length of the altitude of an equilateral triangle of side 33 cm.

Accepted Answer

Let the length of the altitude be h. Then, h = a 3 2 = 3 3 × 3 2 = 4.5

Question 20

A square and rectangle have equal areas. If their perimeters are p and q respectively. Then

Accepted Answer

square and a rectangle with equal areas will satisfy the relation p < q

Area Questions