Area Questions Answers

• 1. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.

  1. \begin{aligned} 120m^2 \end{aligned}
  2. \begin{aligned} 130m^2 \end{aligned}
  3. \begin{aligned} 140m^2 \end{aligned}
  4. \begin{aligned} 150m^2 \end{aligned}

  Answer And Explanation

  Answer: Option A

  Explanation:

  \begin{aligned}
  \text{We know }h^2 = b^2+h^2 \\
  =>\text{Other side }= \sqrt{(17)^2-(15)^2} \\
  = \sqrt{289-225} = \sqrt{64} \\
  = 8 meter \\
  Area = Length \times Breadth \\
  = 15\times8 m^2 = 120 m^2
  
  \end{aligned}

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• 2. 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 And Explanation

  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
  
  

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• 3. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:

  1. 32%
  2. 34%
  3. 42%
  4. 44%

  Answer And Explanation

  Answer: Option D

  Explanation:

  Let original length = x metres and original breadth = y metres.
  
  \begin{aligned}
  \text{Original area } = \text{xy } m^2 \\
  \text{New Length }= \frac{120}{100}x = \frac{6}{5}x \\
  \text{New Breadth }= \frac{120}{100}y = \frac{6}{5}y \\
  =>\text{New Area }= \frac{6}{5}x * \frac{6}{5}y \\
  =>\text{New Area }= \frac{36}{25}xy \\
  
  \text{Area Difference} = \frac{36}{25}xy - xy \\
  = \frac{11}{25}xy \\
  
  Increase \% = \frac{Differnce}{Actual}*100 \\
  = \frac{11xy}{25}*\frac{1}{xy}*100 = 44\%
  
  \end{aligned}
  
  

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• 4. 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 And Explanation

  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}

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• 5. 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.ft, how many feet of fencing will be required ?

  1. 88 feet
  2. 86 feet
  3. 84 feet
  4. 82 feet

  Answer And Explanation

  Answer: Option A

  Explanation:

  We are given with length and area, so we can find the breadth.
  as Length * Breadth = Area
  => 20 * Breadth = 680
  => Breadth = 34 feet
  
  Area to be fenced = 2B + L = 2*34 + 20
  = 88 feet

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• 6. The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .

  1. 22 cm
  2. 24 cm
  3. 26 cm
  4. 28 cm

  Answer And Explanation

  Answer: Option B

  Explanation:

  We know perimeter of square = 4(side)
  So Side of first square = 40/4 = 10 cm
  Side of second square = 32/4 = 8 cm
  
  Area of third Square = 10*10 - 8*8
  = 36 cm
  
  So side of third square = 6 [because area of square = side*side]
  Perimeter = 4*Side = 4*6 = 24 cm

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• 7. 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 And Explanation

  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}

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