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Quantitative Aptitude

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Total Questions : 2556 | Page 3 of 256 pages
Question 21.

  1. A table-cover 3.5 m × 1.5 m is spread on a table. The cost of the top of the table at Rs 250 per sq. metre if 25 cm of table cover is hanging all round the table is

  1.    Rs 700
  2.    Rs 725
  3.    Rs 750
  4.    Rs 775
 Discuss Question
Answer: Option C. -> Rs 750
Question 22.

  1. The base of a triangular field is \(2\frac{1}{2}\) times its height. If the cost of turiing it at Rs 35 per 100 sq. metres is Rs 700, its base is

  1.    50 m
  2.    100 m
  3.    150 m
  4.    none of these
 Discuss Question
Answer: Option B. -> 100 m
Question 23.

  1. The area of a right isosceles triangle is 12.5 cm2. The length of its equal sides is

  1.    5 cm
  2.    10 cm
  3.    15 cm
  4.    20 cm
 Discuss Question
Answer: Option A. -> 5 cm
Question 24.

  1. The diagonal of a square is twice the side of an equilateral triangle. The ratio of the area of the triangle to the area of the square is

  1.    \(\sqrt{3}:6\)
  2.    \(\sqrt{3}:8\)
  3.    \(\sqrt{3}:10\)
  4.     none of these
 Discuss Question
Answer: Option B. -> \(\sqrt{3}:8\)
Question 25.

  1. From a point in the interior of an equilateral triangle perpendiculars are drawn to the three sides which measure 10, 12, and 18 metres. The area of the triangle is (approximately)

  1.    294 m2
  2.    924 m2
  3.    429 m2
  4.     none of these
 Discuss Question
Answer: Option B. -> 924 m2
Question 26.
  1. In a quadrilateral field ABCD, AB = 8.5 m, BC = 8.5 m, CD = 16.5 m, DA = 14.3 m and AC = 15.4 m. The cost of turfing it at the rate of Rs 1.50 per sq. metre is

  1.    Rs 74.04
  2.    Rs 94.04
  3.    Rs 194.04
  4.    none of these  
 Discuss Question
Answer: Option C. -> Rs 194.04
To find the cost of turfing the field, we need to calculate its area. Since the field is a quadrilateral, we can divide it into two triangles and calculate the area of each triangle using Heron's formula.
Heron's formula states that the area of a triangle with sides a, b, and c is given by:
$A = \sqrt{s(s-a)(s-b)(s-c)}$
where $s$ is the semi-perimeter of the triangle, given by:
$s = \frac{1}{2}(a+b+c)$
Using this formula, we can calculate the area of each triangle, and then add them to get the total area of the field. The semi-perimeter of the first triangle ABC is:
$s_1 = \frac{1}{2}(8.5 + 8.5 + 15.4) = 16.2$
Using Heron's formula, we get:
$A_1 = \sqrt{16.2(16.2-8.5)(16.2-8.5)(16.2-15.4)} \approx 53.57 \text{ m}^2$
Similarly, the semi-perimeter of the second triangle CDA is:
$s_2 = \frac{1}{2}(14.3 + 16.5 + 15.4) = 23.1$
Using Heron's formula, we get:
$A_2 = \sqrt{23.1(23.1-14.3)(23.1-16.5)(23.1-15.4)} \approx 91.17 \text{ m}^2$
The total area of the field is:
$A = A_1 + A_2 \approx 144.74 \text{ m}^2$
Therefore, the cost of turfing the field at the rate of Rs 1.50 per sq. metre is:
Cost = $1.50 \times A \approx Rs 194.04$
Hence, the correct answer is option C.If you think the solution is wrong then please provide your own solution below in the comments section .
Question 27.

  1. The cost of cultivating a quadrilateral field at the rate of 10 paise per sq. metre when its diagonals intersect each other at right angles and measure 48 m and 32 m is

  1.    Rs 76
  2.    Rs 67
  3.    Rs 67.80
  4.    Rs 76.80
 Discuss Question
Answer: Option D. -> Rs 76.80
Question 28.

  1. Number of bricks measuring 25 cm × 16 cm required to pave the floor of a room 8 m long and 5 m wide is

  1.    900
  2.    1000
  3.    1100
  4.    1200
 Discuss Question
Answer: Option B. -> 1000
Question 29.

  1. If the altitude of a rectangle is doubled and its base is kept the same, the area

  1.    Becomes double
  2.    Remains unchanged
  3.    Becomes three times
  4.     none of these
 Discuss Question
Answer: Option A. -> Becomes double
Question 30.

  1. In a right angled triangle with sides a and b, hypotenuse c, the altitude drawn on the hypotenuse is x. Then,

  1.    ab = x2
  2.    a2 + b2 + = 2x2
  3.    \(\frac{1}{a} + \frac{1}{b}=\frac{1}{x}\)
  4.    \(\frac{1}{a^{2}} + \frac{1}{b^{2}}=\frac{1}{x^{2}}\)
 Discuss Question
Answer: Option D. -> \(\frac{1}{a^{2}} + \frac{1}{b^{2}}=\frac{1}{x^{2}}\)

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