Mathematics · Quantitative Aptitude

Mensuration and Area

83 Questions

Mensuration and area problems cover calculating dimensions of 2D geometric figures. Questions involve finding areas for trapeziums, squares, and hexagons using standard formulas. This arithmetic topic consistently appears in quantitative aptitude tests for competitive exams.

Trapezium areaSquare dimensionsHexagon propertiesParallelogram areaGeometric conversions

Mensuration and Area Questions

Multiple choice

What is the area of a regular hexagon with side length 6?

  1. 36\sqrt{3}

  2. 72\sqrt{3}

  3. 108\sqrt{3}

  4. 144\sqrt{3}
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The area of a regular hexagon with side length s is given by the formula (A = \frac{3\sqrt{3}}{2}s^2). Substituting s = 6 into the formula, we get: (A = \frac{3\sqrt{3}}{2} \cdot 6^2 = \frac{3\sqrt{3}}{2} \cdot 36 = 108\sqrt{3}). Therefore, the area of the regular hexagon is 108\sqrt{3}.

Multiple choice

A regular hexagon has side length 6 cm. What is the area of the hexagon?

  1. 36√3 cm²

  2. 72√3 cm²

  3. 108√3 cm²

  4. 144√3 cm²
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of a regular hexagon with side length 'a' is given by (3√3 / 2) * a². Substituting a = 6 cm, we get the area as (3√3 / 2) * 6² = 72√3 cm².

Multiple choice

What is Brahmagupta's formula for the area of a cyclic quadrilateral?

  1. $$A = \sqrt{(s-a)(s-b)(s-c)(s-d)}$$
  2. $$A = \frac{1}{2}ab$$
  3. $$A = \frac{1}{2}bh$$
  4. $$A = \frac{1}{2}lw$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's formula for the area of a cyclic quadrilateral is given by $$A = \sqrt{(s-a)(s-b)(s-c)(s-d)}$$, where $$s$$ is the semiperimeter of the quadrilateral and $$a, b, c, d$$ are the lengths of its sides.

Multiple choice

Find the surface area of a rectangular prism with length 5 cm, width 3 cm, and height 2 cm.

  1. 52 cm²

  2. 30 cm²

  3. 20 cm²

  4. 10 cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a rectangular prism is given by SA = 2(lw + wh + lh), where l is the length, w is the width, and h is the height. In this case, l = 5 cm, w = 3 cm, and h = 2 cm, so SA = 2((5 * 3) + (3 * 2) + (5 * 2)) = 52 cm².

Multiple choice

Brahmagupta's theorem states that the area of a cyclic quadrilateral is given by: $K = \sqrt{(s-a)(s-b)(s-c)(s-d)}$, where $s$ is the semi-perimeter and $a$, $b$, $c$, and $d$ are the lengths of the sides of the quadrilateral. What is the value of $s$ in terms of the side lengths?

  1. $s = \frac{a + b + c + d}{2}$
  2. $s = \frac{a + b - c - d}{2}$
  3. $s = \frac{a - b + c - d}{2}$
  4. $s = \frac{a - b - c + d}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The semi-perimeter of a quadrilateral is half the sum of its side lengths, which is given by the formula $s = \frac{a + b + c + d}{2}$.

Multiple choice

What is the formula for calculating the area of a cyclic quadrilateral using Brahmagupta's formula?

  1. $$Area = \sqrt{(s - a)(s - b)(s - c)(s - d)}$$
  2. $$Area = \frac{1}{2}absinC$$
  3. $$Area = \frac{1}{2}bh$$
  4. $$Area = \frac{1}{2}lw$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's formula for calculating the area of a cyclic quadrilateral is given by the formula $$Area = \sqrt{(s - a)(s - b)(s - c)(s - d)}$$, where 's' is the semi-perimeter of the quadrilateral and 'a', 'b', 'c', and 'd' are the lengths of its sides.

Multiple choice

What is the formula for the surface area of a pyramid?

  1. $S = Bh + \frac{1}{2}Pl$
  2. $S = Bh + Pl$
  3. $S = Bh - \frac{1}{2}Pl$
  4. $S = Bh - Pl$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for the surface area of a pyramid is $S = Bh + \frac{1}{2}Pl$, where B is the area of the base of the pyramid, h is the height of the pyramid, P is the perimeter of the base of the pyramid, and l is the slant height of the pyramid.

Multiple choice

What is the formula for the surface area of a prism?

  1. $S = 2Bh + Pl$
  2. $S = Bh + Pl$
  3. $S = Bh - Pl$
  4. $S = 2Bh - Pl$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for the surface area of a prism is $S = 2Bh + Pl$, where B is the area of the base of the prism, h is the height of the prism, P is the perimeter of the base of the prism, and l is the slant height of the prism.

Multiple choice

What is the formula for the surface area of a rectangular prism with length (l), width (w), and height (h)?

  1. \(2(lw + wh + lh)\)
  2. \(lw + wh + lh\)
  3. \(2(l^2 + w^2 + h^2)\)
  4. \(l^2 + w^2 + h^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a rectangular prism is given by the formula (2(lw + wh + lh)), where (l) is the length, (w) is the width, and (h) is the height of the prism.

Multiple choice

What is Brahmagupta's formula for the area of a cyclic quadrilateral?

  1. $$A = \sqrt{(s - a)(s - b)(s - c)(s - d)}$$
  2. $$A = \frac{1}{2}absinC$$
  3. $$A = \frac{1}{2}bh$$
  4. $$A = \frac{1}{2}lw$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's formula for the area of a cyclic quadrilateral is given by $$A = \sqrt{(s - a)(s - b)(s - c)(s - d)}$$, where $$s$$ is the semiperimeter of the quadrilateral and $$a, b, c, d$$ are the lengths of its sides.

Multiple choice

What is Brahmagupta's rule for finding the area of a cyclic quadrilateral?

  1. The area of a cyclic quadrilateral is equal to the product of its diagonals.

  2. The area of a cyclic quadrilateral is equal to half the product of its diagonals.

  3. The area of a cyclic quadrilateral is equal to the sum of the areas of its triangles.

  4. The area of a cyclic quadrilateral is equal to the difference of the areas of its triangles.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Brahmagupta's rule for finding the area of a cyclic quadrilateral states that the area of a cyclic quadrilateral is equal to half the product of its diagonals.

Multiple choice

The formula for calculating the surface area of a pyramid is:

  1. S = B + L

  2. S = 2 * B + L

  3. S = 4 * B + L

  4. S = B + 2 * L
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the surface area of a pyramid is S = B + L, where B is the area of the base of the pyramid and L is the sum of the areas of the triangular faces of the pyramid.

Multiple choice

The formula for calculating the surface area of a prism is:

  1. S = 2 * B + P * h

  2. S = B + P * h

  3. S = 4 * B + P * h

  4. S = B + 2 * P * h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the surface area of a prism is S = 2 * B + P * h, where B is the area of the base of the prism, P is the perimeter of the base of the prism, and h is the height of the prism.

Multiple choice

What is the area of a regular hexagon with a side length of $6$ cm?

  1. $36\sqrt{3}$ cm$^2$
  2. $72\sqrt{3}$ cm$^2$
  3. $108\sqrt{3}$ cm$^2$
  4. $144\sqrt{3}$ cm$^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a regular hexagon with a side length $s$ is given by the formula $A = \frac{3\sqrt{3}}{2}s^2$. Substituting the given value, we get $A = \frac{3\sqrt{3}}{2}(6)^2 = 36\sqrt{3}$ cm$^2$.

Multiple choice

What is the formula for calculating the area of a field using trigonometry?

  1. Area = (1/2) * base * height

  2. Area = (1/2) * base * sine(theta)

  3. Area = (1/2) * base * cosine(theta)

  4. Area = (1/2) * base * tangent(theta)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a field can be calculated using the formula Area = (1/2) * base * height, where 'base' is the length of the base of the field and 'height' is the length of the altitude drawn from the vertex opposite the base.