Area Questions and Answers

• 22. 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 ?

  1. 18 meter
  2. 20 meter
  3. 22 meter
  4. 25 meter

  Answer :

  Option B

  Explanation:

  Let breadth =x metres.
  Then length =(115x/100)metres.
  \begin{aligned}
  =x*\frac{115x}{100}= 460\\
  x^2=(460 x 100/115) \\
  x^2=400 \\
  x= 20 \\
  \end{aligned}

• 23. The area of a square is 69696 cm square. What will be its diagonal ?

  1. 373.196 cm
  2. 373.110 cm
  3. 373.290 cm
  4. 373.296 cm

  Answer :

  Option D

  Explanation:

  If area is given then we can easily find side of a square as,
  \begin{aligned}Side = \sqrt{69696} \\
  = 264 cm \\
  \text{we know diagonal =}\sqrt{2}\times side \\
  = \sqrt{2}\times 264 \\
  = 1.414 \times 264 \\
  = 373.296 cm \end{aligned}

• 24. The length of a rectangle is three times of its width. If the length of the diagonal is \begin{aligned}8\sqrt{10}\end{aligned}, then find the perimeter of the rectangle.

  1. 60 cm
  2. 62 cm
  3. 64 cm
  4. 66 cm

  Answer :

  Option C

  Explanation:

  Let Breadth = x cm,
  then, Length = 3x cm
  \begin{aligned}
  x^2+{(3x)}^2 = {(8\sqrt{10})}^2 \\
  => 10x^2 = 640 \\
  => x = 8 \\
  \end{aligned}
  So, length = 24 cm and breadth = 8 cm
  Perimeter = 2(l+b)
  = 2(24+8) = 64 cm

• 25. A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.

  1. 10 m * 5 m
  2. 15 m * 5 m
  3. 20 m * 5 m
  4. 25 m * 5 m

  Answer :

  Option C

  Explanation:

  From the question, 2b+l = 30
  => l = 30-2b
  \begin{aligned}
  Area = 100m^2 \\
  => l \times b = 100 \\
  => b(30-2b) = 100 \\
  b^2 - 15b + 50 = 0 \\
  =>(b-10)(b-5)=0 \\
  \end{aligned}
  b = 10 or b = 5
  when b = 10 then l = 10
  when b = 5 then l = 20
  Since the garden is rectangular so we will take value of breadth 5.
  So its dimensions are 20 m * 5 m

• 26. What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ?

  1. 1:1
  2. 1:2
  3. 2:3
  4. 2:1

  Answer :

  Option D

  Explanation:

  As far as questions of Area or Volume and Surface area are concerned, it is all about formulas and very little logic. So its a sincere advice to get all formulas remembered before solving these questions.
  
  Lets solve this,
  
  \begin{aligned}
  \text{Area of rectangle =}l*b\\
  \text{Area of triangle =}\frac{1}{2}l*b\\
  \text{Ratio =}l*b:\frac{1}{2}l*b \\
  = 1:\frac{1}{2} \\
  = 2:1
  
  \end{aligned}
  
  One little thing which should be taken care in this type of question is, be sure you are calculating ration in the given order of the question.
  If it is ratio of triangle and rectangle then we have to write triangle formula first. cheers :)

• 27. The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.

  1. 4:25
  2. 4:15
  3. 3:25
  4. 3:15

  Answer :

  Option A

  Explanation:

  Let the diagonals of the squares be 2x and 5x.
  Then ratio of their areas will be
  \begin{aligned}
  \text{Area of square} = \frac{1}{2}*{Diagonal}^2 \\
  \frac{1}{2}*{2x}^2:\frac{1}{2}*{5x}^2 \\
  4x^2:25x^2 = 4:25
  \end{aligned}

• 28. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

  1. \begin{aligned} 152600 m^2\end{aligned}
  2. \begin{aligned} 153500 m^2\end{aligned}
  3. \begin{aligned} 153600 m^2\end{aligned}
  4. \begin{aligned} 153800 m^2\end{aligned}

  Answer :

  Option C

  Explanation:

  Question seems to be typical, but trust me it is too easy to solve, before solving this, lets analyse how we can solve this.
  We are having speed and time so we can calculate the distance or perimeter in this question.
  Then by applying the formula of perimeter of rectangle we can get value of length and breadth, So finally can get the area. Lets solve it:
  
  Perimeter = Distance travelled in 8 minutes,
  => Perimeter = 12000/60 * 8 = 1600 meter. [because Distance = Speed * Time]
  
  As per question length is 3x and width is 2x
  We know perimeter of rectangle is 2(L+B)
  So, 2(3x+2x) = 1600
  => x = 160
  So Length = 160*3 = 480 meter
  and Width = 160*2 = 320 meter
  
  Finally, Area = length * breadth
  = 480 * 320 = 153600