Menstruation

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Mensuration


  • Rectangle

Area = lb
Perimeter = 2(l+b)

  • Square
    Area = a×a
    Perimeter = 4a
  • Parallelogram
    Area = l × h
    Perimeter = 2(l+b)
  • Triangle
    Area =b×h/2
  • Right angle Triangle
    Area =1/2(bh)
    Perimeter = b+h+d
  • Isosceles Right Angle Triangle
    Area = 1/2. a2
    Perimeter = 2a+d
  • Trapezium
    Area = 1/2h(a+b)
    Perimeter = Sum of all sides
  • Rhombus
    Area = d1 × d2/2
    Perimeter = 4l
  • Quadrilateral
    Area =1/2 × Diagonal × (Sum of offsets)
  • Kite
    Area = d1×d2/2
    Perimeter = 2 × Sum on non-adjacent sides

Ques1. If the sides of a triangle are 16cm, 14cm and 10cm. What is its area?

  • 70cm2 ) 130cm2                        c.) 120cm2                       d.) 150cm2                       e.) None of these

Explanation: Answer is A

The triangle with sides 16 cm, 14 cm and 10cm is right angles, where the hypotenuse is 16cm.

Area of the triangle = ½ * 14 * 10 = 70 cm2

Ques2. The perimeter of a triangle is 18 cm and the inradius of the triangle is 2 cm. What is the area of the triangle?

  • 25 cm2 ) 18 cm2                          c.) 20 cm2                             d.) 19 cm2                        e.) None of these

Explanation: Answer is B

Area of triangle = r * s

Where, r is the inradius and s is the semi perimeter of the triangle.

Area of triangle = 2 * 18/2 = 18 cm2

Ques3. Find the area of trapezium whose parallel sides are 10 cm and 8 cm long and the distance between them is 5 cm.

  • 25 cm2                      ) 75 cm2                          c.) 85 cm2                          d.) 45 cm2                               e.) None of these

Explanation: Answer is D

Area of trapezium = ½ (sum of parallel sides) * (perpendicular distance between them)

= ½ (10 + 8) * (5) = 45 cm2

Ques4. Find the area of parallelogram with base 14 cm and height 6 cm.

  • 62 cm2 ) 84 cm2                     c.) 92 cm2                     d.) 31 cm2                            e.) None of these

Explanation: Answer is B

Area of parallelogram = base * height = 14 * 6 = 84 cm2

Ques5. The ratio of the length and the breadth of a rectangle is 3:2 and the area of the rectangle is 2400 sq cm. Find the ratio of the breadth and the area of the rectangle.

  • 1:96 ) 1:48                         c.) 1:60                          d.) 1:68                        e.) None of these

Explanation: Answer is C

Let the length and breadth of the rectangle be 3x and 2x respectively.

(3x) (2x) = 2400

6x2 = 2400

x2 = 400 = 4 * 100 = 22 * 102 (x>0)

  • x = 2 * 10 = 20
  • Ratio of the breadth and the areas = 2x : 6x2 = 1:3x = 1:60

Ques6. The length of a rectangular plot is twice its breadth. If the area of the rectangular plot is 288 sq m, then what is the breadth of the rectangular plot?

  • 12 m ) 17 m                        c.) 14 m                        d.) 11 m                          e.) None of these

Explanation: Answer is A

Let the breadth of the plot be x m.

Length of the plot = 2 x m

(2x) (x) = 288

2x2 = 288

x2 = 144 = 122(x>0)

x = 12 m.

Ques7. The length of parallel sides of a trapezium is 1.5m and 2.5m respectively and perpendicular distance between parallel lines is 6.5m. What is the area of this trapezium?

  • 14m2 ) 13m2                          c.) 15m2                          d.) 18m2                         e.) None of these

Explanation: Answer is B

Here, a = 2.5m, b = 1.5m, h = 6.5m

∴ Area of trapezium =  (a + b) * h =  (2.5 + 1.5) * 6.5 = 13m2

Ques8. What will be the cost of building a fence around a square plot with area equal to 256 sq ft, if the price per foot of building the fence is Rs. 48?

  • 3072 b.) Rs.3828                      c.) Rs.4176                     d.) Rs.5076                   e.) None of these

Explanation: Answer is A

Let the side of the square plot be a ft.

x2 = 256 => x = 16

length of the fence = Perimeter of the plot = 4x = 64 ft.

cost of building the fence = 64 * 48 = Rs.3072

Ques9. The area of a square is equal to four times the area of a rectangle of dimensions 96 * 64 cm. What is the perimeter of the square?

  • 600 cm ) 800 cm                       c.) 768 cm                        d.) 1000 cm                        e.) None of these

Explanation: Answer is C

Area of the square = s*s = 4(96 * 64)

  • s = 24 * 8 = 192 cm
  • Perimeter of the square = 4 * 192 = 768 cm

Ques10. A wire in the form of a circle of radius 4.2 m is bent in the form of a rectangle, whose length and breadth are in the ratio of 5:4. What is the area of the rectangle?

  • 1 cm2 b.) 39.2 cm2                       c.) 45.3 cm2                       d.) 15 cm2                       e.) None of these

Explanation: Answer is

The circumference of the circle is equal to the perimeter of the rectangle

Let l = 5x and b = 4x

  • 2(5x + 4x) = 2 * 22/7 * 4.2
  • x = 1.4

Therefore, l = 7cm and b = 5.6 cm

Area of the rectangle = 7 * 5.6 = 39.2 cm2

Ques11. The area of a square is 1024 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 14 cm less than the side of the square.

  • 18:5            ) 7:16                         c.) 5:14                          d.) 5:32                          e.) None of these

Explanation: Answer is

Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be x cm.

x2 = 1024 = 210

x = (210)1/2 = 25 = 32

L = 2x and b = x – 14

b:l = x – 14 : 2x = 18 : 64 = 9:32

Ques12. The parameter of a square is equal to the perimeter of a rectangle of length 14 cm and breadth 12 cm. Find the circumference of a semi circle whose diameter is equal to the side of the square.

  • 14 cm b.) 47.14 cm                         c.) 84.92 cm                            d.) 20.42 cm                       e.) None of these

Explanation: Answer is D

Let the side of the square be x cm.

Parameter of the rectangle = 2(14 + 12) = 52 cm


Parameter of the square = 52 cm i.e. 4x = 52

x = 13

Diameter of the semicircle = 13cm

Circumference of the semicircle = ½ * 22/7 * 13 = 20.42 cm

Ques13. A cube of side two meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?

  • 80    ) 800                        c.) 8000                        d.) 80000                     e.) None of these

Explanation: Answer is C

Along one edge, the number of small cubes that can be cut = 200/10 = 20

Along each edge 20 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 20 * 20 * 20 = 8000

 

Ques14. The dimensions of a room are 24 feet * 14 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 4 per sq feet if there is one door of dimensions 5 feet * 2 feet and three windows of dimensions 3 feet * 2 feet each?

  • 4800 b.) Rs.3536                          c.) Rs.3500                          d.) Rs.4500                        e.) None of these

Explanation: Answer is B

Area of the four walls = 2h(l+b)

Since, there are doors and windows, area of the walls = 2 * 12(14 + 24) – (5 * 2) – 3(3 * 2) = 884

Total cost = 884 * 4 = Rs.3536

Ques15. The radius of a wheel is 21.7cm. What is the distance covered by the wheel in making 400 resolutions.

  • 60 m b.) 704.20 m                          c.) 352.40 m                             d.) 808.80 m                       e.) None of these

Explanation: Answer is

In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 400 resolutions.

= 400 * 2 * 22/7 * 21.7 = 54560 = 545.60 m

Ques16. The volumes of two cones are in the ratio 1:5 and the radii of the cones are in the ratio of 1:2. What is the length of the wire?

  • 2:5 ) 1:5                         c.) 3:5                         d.) 4:5                           e.) None of these

Explanation: Answer is D

The volume of the cone = (1/3)h

Only radius and height are varying so, ignore (1/3)

V1V2 = r12h1/ r22h2 => 1/5 = (1)2h1/(2)2h2

  • h1/h2 = 4/5

i.e. h1 : h2 = 4:5

Ques17. Find the area of a rhombus whose side is 20 cm and one of the diagonals is 24 cm?

  • 225 sq m ) 384 sq m                       c.) 720 sq m                         d.) 480 sq m                                e.) None of these

Explanation: Answer is B

B

 

 

A                                            C

 

 

D

Consider the rhombus ABCD. Let the diagonals intersect at E. since diagonals bisect at right angles in a rhombus.

BE2 + AE2 = AB2

202 = 122 + AE2AE =  = 16

AC = 16 + 16 = 32 cm

Area of rhombus = ½ * d1d2

= ½ * 32 * 24 = 384 sq cm

Ques18. The length of a rectangle is two-fourth of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1156 sq units. What is the area(in sq units) of the rectangle if the breadth is 10 units?

  • 140 ) 156                           c.) 175                            d.) 214                           e.) None of these

Explanation: Answer is

Given that the area of the square = 1156 sq units

  • Side of square = = 34 units
  • The radius of the circle = side of the square = 34 units length of the rectangle = 2/4 * 34 = 17 units
  • Given that breadth = 10 units
  • Area of the rectangle = lb = 17 * 10 = 170 sq. units

Ques19. The sector of a circle has a radius of 14 cm and central angle 140. Find its perimeter.

  • 5 cm b.) 63.5 cm                     c.) 64.5 cm                          d.) 62.2 cm                        e.) None of these

Explanation: Answer is

Perimeter of the sector = length of the arc + 2(radius)

= (140/360 * 2 * 22/7 * 14) + 2(14)

= 34.2 + 28 = 62.2 cm

Ques20. The difference between the length and breadth of a rectangle is 13m. If its perimeter is 106m, then its area is:

  • 660 m                     b.) 420 sq m                        c.) 480 sq m                          d.) 520 sq m                      e.) None of these

Explanation: Answer is A

We have (l – b) = 13 and 2(l + b) = 106 or (l + b) = 53

From these two equations we get l = 33 and b = 20

∴ area = (l * b) = (33 * 20) m2 = 660 m2

Ques21. A rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered. If the area of the field is 480 sq feet, how many feet of fencing will be required?

  • 34 ) 40                           c.) 68                           d.) 106                          e.) None of these

Explanation: Answer is D

L = 10ft and lb = 480 sq ft

So, b = 48 ft

∴ Length of fencing = (l + 2b) = (10 + 96) ft = 106 ft.

Ques22. A tank is 15 m long, 6 m wide and 3 m deep. The cost of plastering its walls and bottom at 65 paise per sq m is:

  • 156.5 b.) Rs. 158.6                         c.) Rs. 155                       d.) Rs. 140.4                      e.) None of these

Explanation: Answer is D

Area to be plastered = [2(l + b) * h] + (l * b)

= {[2(15 + 6) * 3] + (15 * 6)} m2

= ( 126 + 90) m2 = 216 m2

∴ Cost of plastering = Rs. Rs. 140.4

Ques23. A towel when bleached, was found to have lost 30% of its length and 20% of its breadth. The percentage of decrease in area is:

  • 30% ) 32%                       c.) 36%                         d.) 28%                           e.) None of these

Explanation: Answer is C

Let original length = x and original breadth = y

Decrease in area = xy –

=

=

∴ Decrease% = % = 36%

Ques24. A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

  • 20 ) 24                          c.) 30                          d.) 33                         e.) None of these

Explanation: Answer is C

Let the side of the square(PQRS) be x meters.

Then, PQ + QR = 2x meters

PR = x = (1.41x) m

Saving on 2x metres = (0.59x) m

Saving % = = 30% approx..

Ques25. The diagonal of a rectangle is  cm and its area is 17 sq cm. The perimeter of the rectangle must be:

  • 9 cm ) 16 cm                         c.) 20 cm                          d.) 41 cm                           e.) None of these

Explanation: Answer is B

=

lb = 17

(l + b)2 = (l2 + b2) + 2lb = 30 + 34 = 64

  • (l + b) = 8

∴ Perimeter = 2(l+b) = 16 cm