Question 1

If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.

Accepted Answer

Let x and y be the length and breadth of the rectangle respectively. Then, x - 4 = y + 3 or x - y = 7 ----(i) Area of the rectangle =xy; Area of the square = (x - 4) (y + 3) (x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(ii) Solving (i) and (ii), we get x = 16 and y = 9. Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.

Question 2

The no of revolutions a wheel of diameter 40cm makes in traveling a distance of 176m is

Accepted Answer

distance covered in 1 revolution = 2 πr = 2 x (22/7) x 20 = 880/7 cm required no of revolutions = 17600 x (7/880) = 140

Question 3

A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius of the pool is?

Accepted Answer

let the radius of the pool be Rft Radius of the pool including the wall = (R+4)ft Area of the concrete wall = π R + 4 2 - R 2 = π R + 4 + R R + 4 - R = 8 π R + 2 sq feet => 8 π R + 2 = 11 25 πR 2 = > 11 R 2 = 200 R + 2 Radius of the pool R = 20ft

Question 4

The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m.What is the area of the field?

Accepted Answer

Let length = x meters, then breadth = 0.6x Given that perimeter = 800 meters => 2[ x + 0.6x] = 800 => x = 250 m Length = 250m and breadth = 0.6 x 250 = 150m Area = 250 x 150 = 37500 sq.m

Question 5

A typist uses a sheet measuring 20cm by 30cm lengthwise.If a margin of 2 cm is left on each side and a 3 cm margin on top and bottom, then percent of the page used for typing is

Accepted Answer

Area of the sheet = 20 × 30 c m 2 Area used for typing = 20 - 4 × 30 - 6 c m 2 required % = 384 600 × 100 =64%

Question 6

The difference between circumference and semidiameter of a circle is 37 cm. What is the diameter of the circle ?

Accepted Answer

circumference of a circle = 2 π r => 2 × 22/7 × r – r = 37 => 37/7 × r = 37 => r = 7 cm. Diameter D = 2r = 7×2 = 14 cm.

Question 7

A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.

Accepted Answer

Distance covered in one revolution = 88 × 1000 1000 = 88m. 2 πR 2 = 88 ⇒ 2 × 22 7 × R = 88 ⇒ R = 88 × 7 44

Question 8

If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area ?

Accepted Answer

The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle =1/2 x base x height => 1/2 x 24 x 10 = 120 sq.cm

Question 9

Find the area of the square whose side is equal to the diagonal of a rectangle of length 3 cm and breadth 4 cm.

Accepted Answer

Given length of the rectangle = 3 cm Breadth of the rectangle = 4 cm Then, the diagonal of the rectangle D = 3 2 + 4 2 = 25 = 5 Then, it implies side of square = 5 cm We know that Area of square = S x S = 5 x 5 = 25 sq.cm.

Question 10

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 11

The breadth of a rectangular field is 75% of its length. If perimeter of the field is 1050 m, what will be th area of field ?

Accepted Answer

Let the length be 'l' and breadth be 'b'. b = l × 3/4__________(a) 2(l+b) = 1050 l+b = 525___________(b) From equations (a) and (b), l = 300m, b = 225 m Area = l × b = 300 × 225 = 67500 sq.m.

Question 12

The length, breadth and height of a room are in the ratio 7:3:1. If the breadth and height are doubled while the length is halved, then by what percent the total area of the 4 walls of the room will be increased ?

Accepted Answer

Let length, breadth and height of the room be 7, 3, 1 unit respectively. Area of walls = 2(l+b)xh = 2(7+3)x1 = 20 sq. unit. Now, length, breadth and height of room will become 3.5, 6 and 2 respectively. Area of walls = 2(l+b)xh = 2(3.5+6)x2 = 38 sq. unit. % Increase in the area of walls = (38-20)x100/20 = 90%.

Question 13

How many square units in 13 by 9?

Accepted Answer

Number of square units in 13 by 9 is given by the area it forms with length and breadth as 13 & 9 Area = 13 x 9 = 117 Hence, number of square units in 13 by 9 is 117 sq.units.

Question 14

In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.

Accepted Answer

Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively. Then, 1 2 × x × 3 h 1 2 × y × 4 h = 4 3 ⇒ x y = 4 3 × 4 3 = 16 9 Required ratio = 16 : 9.

Question 15

The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.40 per metre.

Accepted Answer

Area = (13.86 x 10000) sq.m = 138600 sq.m πR 2 = 138600 ⇒ R 2 = 138600 × 7 22 ⇒ R = 210 m Circumference = 2 πR 2 = 2 × 22 7 × 210 = 1320 m Cost of fencing = Rs. (1320 x 4.40) = Rs. 5808.

Question 16

A semicircular shaped window has diameter of 63cm. Its perimeter equals

Accepted Answer

perimeter of window = π r+2r = [(22/7) x (63/2) + 63] = 99+63 = 162 cm

Question 17

A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is

Accepted Answer

Let the triangle and parallelogram have common base b, let the Altitude of triangle is h1 and of parallelogram is h2(which is equal to 100 m), then Area of triangle = 1 2 × b × h 1 Area of rectangle = b*h2 As per Given, 1 2 * b * h 1 = b * h 2 1 2 * b * h 1 = b * 100 h1=200

Question 18

What is the area of an obtuse angled triangle given below with two sides are 8 and 12 and the angle included between two sides is 150 deg?

Accepted Answer

We know that, The area of a triangle with two sides given and included angle A = 1/2 x product of sides x Sin(angle) Here the two sides are 8 & 12 Angle = 150 Area = 1/2 x 8 x 12 x sin150 Sin(150) = sin(90+60) = cos(60) = 1/2 A = 48 x 1/2 = 24 Area of the given triangle = 24 sq units.

Question 19

A sector of 120 degrees, cut out from a circle, has an area of 66/7 sq cm. Find the radius of the circle.

Accepted Answer

πr = 66 7 r =3

Question 20

The length of the room is 5.5m and width is 3.75m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq meter

Accepted Answer

l=5.5m w=3.75m area of the floor = 5.5 x 3.75 = 20.625 sq m cost of paving = 800 x 20.625 = Rs. 16500

Area Questions