Question 1

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

Accepted Answer

Area = 5.5 × 3.75 sq. metre. Cost for 1 sq. metre. = Rs. 800 Hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = Rs. 16500

Question 2

The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

Accepted Answer

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103. Solving the two equations, we get: l = 63 and b = 40. Area = (l x b) = (63 x 40) = 2520 sq.m

Question 3

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

Accepted Answer

Let inner radius be r metres. Then, 2 π r = 440 ; r = 440 × 7 44 = 70 m. Radius of outer circle = (70 + 14) m = 84 m.

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 area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field?

Accepted Answer

Let breadth=x meters. Then, Length = 115 x 100 meters Given that, x × 115 x 100 = 460 => x = 20 Breadth = 20

Question 6

A circular piece of thin wire is converted into a rhombus of side 11 cm. Find the diameter of the circular piece?

Accepted Answer

Circular piece is 4 x 11 = 44 cm long, Then Circumference of circle is given by, 44 = pi x D, where D is the diameter D = 44 / pi Take pi = 22 / 7, then D = 44 / (22/7) = (44 x 7) / 22 D = 14 cm.

Question 7

The area of a circle of radius 5 is numerically what percent its circumference?

Accepted Answer

required percentage = πr 2 2 πr × 100 = 250 %

Question 8

Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq meters.

Accepted Answer

clearly the cow will graze a circular field of area 9856 sq m and radius equal to the length of the rope. Let the length of the rope be r mts then, πr 2 = 9856 ⇒ r 2 = 9856 × 7 22 = 3136 ⇒ r = 56 m

Question 9

Square units 13 by 9 of an office area is

Accepted Answer

Square units 13 by 9 of an office means office of length 13 units and breadth 9 units. Now its area is 13x 9 = 117 square units or units square.

Question 10

Find the area of the trapezium, whose parallel sides are 12 cm and 10 cm, and distance between the parallel sides is 14 cm?

Accepted Answer

We know that, Area of trapezium = 1/2 x (Sum of parallel sides) x (Distance between Parallel sides) = 1/2 x (12 + 10) x 14 = 22 x 14/2 = 22 x 7 = 154 sq. cm

Question 11

The area of the circle is 220 sq.m, the area of the square inscribed in a circle will be

Accepted Answer

area of a square = 1 2 d i a g o n a l 2

Question 12

The difference between two parallel sides of a trapezium is 4 cm. perpendicular distance between them is 19 cm. If the area of the trapezium is 475 find the lengths of the parallel sides.

Accepted Answer

Let the two parallel sides of the trapezium be a cm and b cm. Then, a - b = 4 And, 1 2 × a + b × 19 = 475 = > a + b = 50 Solving (i) and (ii), we get: a = 27, b = 23. So, the two parallel sides are 27 cm and 23 cm.

Question 13

The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

Accepted Answer

Let breadth = x metres. Then, length = (x + 20) metres. Perimeter =5300/23.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m.

Question 14

Find the ratio of the areas of the incircle and circumcircle of a square.

Accepted Answer

Let the side of the square be x. Then, its diagonal = 2 x 2 = 2 x Radius of incircle = x 2 Radius of circum circle= 2 × x 2 = x 2 Required ratio = πx 2 4 : πx 2 2 = 1 4 : 1 2 = 1 : 2

Question 15

The perimeter of a rectangle whose length is 6 m more than its breadth is 84 m. What will be the area of the rectangle?

Accepted Answer

Let the breadth of the rectangle = b mts Then Length of the rectangle = b + 6 mts Given perimeter = 84 mts 2(L + B) = 84 mts 2(b+6 + b) = 84 2(2b + 6) = 84 4b + 12 = 84 4b = 84 - 12 4b = 72 b = 18 mts => Length = b + 6 = 18 + 6 = 24 mts Now, required Area of the rectangle = L x B = 24 x 18 = 432 sq. mts

Question 16

What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad?

Accepted Answer

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = 41 × 41 c m 2 Required number of tiles = 1517 × 902 41 × 41 = 814

Question 17

A rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?

Accepted Answer

perimeter of the plot = 2(90+50) = 280m no of poles =280/5 =56m

Question 18

The length and the breadth of rectangular field are in the ratio of 8 : 7. If charges of the painting the boundary of rectangle is at Rs. 10 per meter is Rs. 3000. What is the area of rectangular plot?

Accepted Answer

Perimeter of the rectangle is given by 3000/10 = 300 mts But we know, The Perimeter of the rectangle = 2(l + b) Now, 2(8x + 7x) = 300 30x = 300 x = 10 Required, Area of rectangle = 8x x 7x = 56 x 100 = 5600 sq. mts.

Area Questions