Question 1

If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is:

Accepted Answer

A square and a rhombus on the same base are equal in area

Question 2

A rectangular parking space is marked out by painting three of its sides.If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?

Accepted Answer

Let l = 9 ft. Then l + 2b = 37 => 2b = 37 – l = 37 – 9 = 28 b = 28/2 = 14 ft. Area = lb = 9 × 14 = 126 sq. ft.

Question 3

The length of a rope in meter by which a cow must be tethered in order that she may be able to graze an area of 2826 sq.m is ?

Accepted Answer

The cow can graze an area of 2826 sq.m i.e it is able to cover area of circle of 2826 sq.m Therefore, πr 2 =2826 r 2 =(2826×7/22) = 899.18 = 900 r = 30 m. Therefore, the radius of the circle implies the length of the rope = 30 mts.

Question 4

An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of c…

Accepted Answer

Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 x 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40

Question 5

In a rectangle, length is three times its breadth. If the length and the breadth of the rectangle are increased by 30% and 100% respectively, then its perimeter increases by

Accepted Answer

Let the breadth of the rectangle = x Length of the the rectangle will be = 3 times of breadth = 3x So the initial perimeter = 2(length + breadth) = 2(x + 3x) = 8x New breadth after increase = x + 10x/100 = 1.1x New length after increase = 3x + 30*3x/100 = 3.9x New perimeter = 2(1.1x + 3.9x) = 10x Percentage change in perimeter = ( 10x-8x)*100/8x = 25%

Question 6

A rectangular grassy plot 110m by 65cm has a gravel path .5cm wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq.mt

Accepted Answer

area of theplot = 110 * 65 = 7150 sq.m area of the plot excluding the path = (110-5)* (65-5) = 6300 sq.m area of the path = 7150 - 6300 =850 sq.m cost of gravelling the path = 850 x (80/100) = 680 Rs

Question 7

The ratio of bases of two triangles is x:y and that of their areas is a:b. Then the ratio of their corresponding altitudes wll be

Accepted Answer

a : b =(1/2 * x * H) : (1/2 * y * h) bxH = ayh => H/h =ay/bx Hence H:h = ay:bx

Question 8

If each side of a square is increased by 25%, find the percentage change in its area.

Accepted Answer

Let each side of the square be a. Then, area = . a 2 New side = 125 a 100 = 5 a 4 . New area = 5 a 4 2 = 25 a 2 16 Increase in area = 25 a 2 16 - a 2 = 9 a 2 16 Increase% = 9 a 2 16 * 1 a 2 * 100 % = 56.25%.

Question 9

If the perimeters of a square and a rectangle are the same, then the area a & b enclosed by them would satisfy the condition:

Accepted Answer

Take a square of side 4cm and a rectangle having l=6cm and b=2cm then perimeter of square = perimeter of rectangle area of square = 16 sq.cm area of rectangle = 12 sq.cm Hence a >b

Question 10

The area of a square field is 69696sq.cm..its diagonal will be equal to

Accepted Answer

d = 2 * s = > d = 2 * 69696

Question 11

What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?

Accepted Answer

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = (41 x 41) sq.cm Required number of tiles =1517 x 902/(41 x 41) = 814.

Question 12

The area of a field in the shape of a trapezium measures 1440sq m. The perpendicular distance between its parallel sides is 24cm. If the ratio of the sides is 5:3, the length of the longer parallel side is:

Accepted Answer

Area of field = 1 2 * 5 x + 3 x * 24 = 96x sq.m 96x = 1440 => x = 1440 96 = 15 Hence, the length of longer parallel side = 5x = 75m

Question 13

A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper?

Accepted Answer

when folded along the breadth we have 2(l/2 +b) = 34 or l+2b = 34...........(1) when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2) from 1 &2 we get l=14 and b=10 Area of the paper = 14*10 = 140 sq cm

Question 14

The perimeter of a square is 40 meters. Find the length of one side of the square

Accepted Answer

P = 4 x s

Question 15

The perimeter of a rectangle is 160 cm. The rectangle is 4 times longer than wide. What are the length and width of this rectangle?

Accepted Answer

P=2(l+b) l=4b

Question 16

A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

Accepted Answer

Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3,4,5 triangle and is therefore, 5. Circumference = π.diameter = 5π

Question 17

A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?

Accepted Answer

The measure of the third side of a triangle must lie between the sum and the difference of the other two sides. Using this fact along with the answer choices, we can eliminate the wrong answers. Option A cannot be correct because 4 would not be the longest side.(sides 4, 5, and 4) Option B could be correct because the other two sides would be 3 and 4. Option C cannot be correct because this third side would be greater than the sum of the other two sides.

Question 18

2 metres broad pathway is to be constructed around a rectangular plot on the inside. The area of the plots is 96 sq.m. The rate of construction is Rs. 50 per square metre. Find the total cost of the construction?

Accepted Answer

Given lb =96 Area of pathway = [(l-4)(b-4)-lb] = 16-4(l+b) Which cannot be determined. so, data is inadequate.

Area Questions