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Area - Quiz

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The percentage of error in the calculated area of the square, given that an error of 2% in excess was made while measuring the side, is:

  • A2%
  • B2.02%
  • C4%
  • D4.04%

What is the area of a triangle with base 5 meters and height 10 meters?

  • A20 square meters
  • B35 square meters
  • C25 square meters
  • D15 square meters

What is the area of a square field whose diagonal is 16 m?

  • A130 m2
  • B128 m2
  • C126 m2
  • D124 m2

The distance between a rectangle's length and perimeter is 100 cm. What is the rectangle's width?

  • A80 cms
  • B90 cms
  • C50 cms
  • DData inadequate

What is the ratio of the new area to the original area of the square if each side of the square is increased by 50%?

  • A5: 4
  • B2.25 : 1
  • C4: 5
  • D4: 7

What is the decimal equivalent of 5%?

  • A420 cm2
  • B380 cm2
  • C480 cm2
  • D410 cm2

A rectangle's length is three times its width. The area of the rectangle is increased by 81 square cm if its length is reduced by 9 cm and its breadth is increased by 9 cm. Determine the rectangle's length.

  • A9 cm
  • B18 cm
  • C27 cm
  • D28 cm

The diagonals of two squares have a 3:7 ratio. Determine their area ratio.

  • A3 : 17
  • B9 : 49
  • C24 : 35
  • D8 : 23

How many square tiles are needed to pave the floor of a room 30 m 34 cm long and 18 m 4 cm wide?

  • A814
  • B816
  • C700
  • D724

Determine the percentage change in the area of a square if each side is increased by 16%.

  • A34.56 %
  • B32.43 %
  • C29.45 %
  • D45.24 %
Results:
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Area - Quiz

Guest User clock Time Taken:
Questions: Answered: Not Answered:
rightCorrect Answer: wrongWrong Answer: percentage smallPercentage: %

Q: The percentage of error in the calculated area of the square, given that an error of 2% in excess was made while measuring the side, is:

  • A. 2%
  • B. 2.02%
  • C. 4%
  • D. 4.04%
Correct Option: D
Remarks:

Explanation:

The percentage error in the calculated area of the square is 4.04%.
This is calculated by taking the difference between the actual area and the measured area, and then expressing it as a percentage of the actual area.
In this case, the actual area is 100cm x 100cm = 10000 cm2 and the measured area is 102cm x 102cm = 10404 cm2
The difference (10404 - 10000) = 404 cm2 which is 4.04% of the actual area.

Q: What is the area of a triangle with base 5 meters and height 10 meters?

  • A. 20 square meters
  • B. 35 square meters
  • C. 25 square meters
  • D. 15 square meters
Correct Option: C
Remarks:

Explanation:

Triangle area = 12 * base * height
As a result, the area is 12 * 5 * 10 = 25 square metres.

Q: What is the area of a square field whose diagonal is 16 m?

  • A. 130 m<sup>2 </sup>
  • B. 128 m<sup>2 </sup>
  • C. 126 m<sup>2 </sup>
  • D. 124 m<sup>2 </sup>
Correct Option: B
Remarks:

Explanation:
 
Area of a square:
side2 = Area Aptitude × (diagonal)2 

                         = Area Aptitude x 162 

                         = Area Aptitude x 256

                         = 128 m2 
 

Q: The distance between a rectangle's length and perimeter is 100 cm. What is the rectangle's width?

  • A. 80 cms
  • B. 90 cms
  • C. 50 cms
  • D. Data inadequate
Correct Option: D
Remarks:

Explanation:

Let the length of the rectangle be 'x' and breadth of the rectangle be 'y'

According to the question:

2(x + y) - x = 100

2x + 2y - x = 100

x + 2y = 100

From this we cannot find 'y' (breadth), so the given data is inadequate.

Q: What is the ratio of the new area to the original area of the square if each side of the square is increased by 50%?

  • A. 5: 4
  • B. 2.25 : 1
  • C. 4: 5
  • D. 4: 7
Correct Option: B
Remarks:

Explanation:

The ratio between the new area and the original area of the square can be found by using the formula for the area of a square and the percentage increase in the side length.

The original area of the square is s^2, where s is the side length. After the side length is increased by 50%, the new side length is 1.5s.

The new area of the square is (1.5s)^2 = 2.25s^2.

To find the ratio between the new area and the original area, we divide the new area by the original area: 2.25s^2 / s^2 = 2.25.

Therefore, the ratio between the new area and the original area of the square can be represented as 2.25 : 1 which means for every 1 unit of original area, the new area is 2.25 unit.

Q: What is the decimal equivalent of 5%?

  • A. 420 cm<sup>2</sup>
  • B. 380 cm<sup>2</sup>
  • C. 480 cm<sup>2</sup>
  • D. 410 cm<sup>2</sup>
Correct Option: C
Remarks:

Explanation:
Let length = X and breadth = Y. Then,
2 (X + Y) = 92 OR X + Y = 46 AND X^2 + Y^2 = (34)^2 = 1156.
Now, (X + Y)^2 = (46)^2
⇔ (X2 + Y2) + 2XY = 2116 ⇔ 1156 + 2XY = 2116
⇒ XY=480
∴ Area = XY = 480 cm2

Q: A rectangle's length is three times its width. The area of the rectangle is increased by 81 square cm if its length is reduced by 9 cm and its breadth is increased by 9 cm. Determine the rectangle's length.

  • A. 9 cm
  • B. 18 cm
  • C. 27 cm
  • D. 28 cm
Correct Option: A
Remarks:

Explanation:

Let breadth = X. Then, length = 3X.
Then,	(3X - 9) (X + 9) = 3X * X + 81
⇒3X2+27X-9X-81=3X2+81
18X=162
⇒X=9 cm
∴ Length of the rectangle = 9 cm

Q: The diagonals of two squares have a 3:7 ratio. Determine their area ratio.

  • A. 3 : 17
  • B. 9 : 49
  • C. 24 : 35
  • D. 8 : 23
Correct Option: B
Remarks:

Explanation:

Let the diagonals of the squares be 3X and 7X respectively.
Ratio of their areas = (1/2)*(3X)2 :( 1/2)*(7X)2 = 9X2: 49X2 = 9: 49.

Q: How many square tiles are needed to pave the floor of a room 30 m 34 cm long and 18 m 4 cm wide?

  • A. 814
  • B. 816
  • C. 700
  • D. 724
Correct Option: A
Remarks:

Explanation:

Length of largest tile = H.C.F. of 3034 cm and 1804 cm = 82 cm.
Area of each tile = (82 x 82) cm^2.
Required number of tiles  3034x1804/82x82  = 37x22=814.

Q: Determine the percentage change in the area of a square if each side is increased by 16%.

  • A. 34.56 %
  • B. 32.43 %
  • C. 29.45 %
  • D. 45.24 %
Correct Option: A
Remarks:

Explanation:

Let each side of the square be X. Then, area = X^2.
New side =(116X/100) =(29X/25). New area = (29X/25)^2
Increase in area = (29X/25)^2 - X^2 =841/625X^2 - X^2=216/625X^2
⇒ Increase% = [(216/625X^2x1/(X^2))*100] % = 34.56%.

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