Mathematics · Quantitative Aptitude

Mensuration and Area

92 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 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

Find the area of a circle with a radius of 7 cm.

  1. 154 cm²

  2. 168 cm²

  3. 182 cm²

  4. 196 cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a circle is calculated using the formula πr², where π is approximately 3.14 and r is the radius of the circle. In this case, we have π x 7² = 3.14 x 49 = 153.86 cm², which is approximately 154 cm².

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

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.

Multiple choice

What is the area of a parallelogram with a base of 12 cm and a height of 8 cm?

  1. 24 square cm

  2. 48 square cm

  3. 72 square cm

  4. 96 square cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The area of a parallelogram is calculated by multiplying its base by its height. In this case, the area is 12 cm * 8 cm = 96 square cm.

Multiple choice

What is the area of a trapezoid with a base of 10 cm, a top base of 6 cm, and a height of 8 cm?

  1. 32 square cm

  2. 64 square cm

  3. 96 square cm

  4. 128 square cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of a trapezoid is calculated by multiplying the average of its bases by its height. In this case, the average of the bases is (10 cm + 6 cm) / 2 = 8 cm. The area is then 8 cm * 8 cm = 64 square cm.

Multiple choice

What is the area of a square with side length 5 cm?

  1. 25 cm^2

  2. 10 cm^2

  3. 20 cm^2

  4. 15 cm^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a square is given by the formula A = s^2, where s is the length of a side. In this case, s = 5 cm, so A = 5^2 = 25 cm^2.

Multiple choice

A square has an area of 36 cm^2. What is the length of each side?

  1. 6 cm

  2. 8 cm

  3. 9 cm

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

The area of a square is given by the formula A = s^2, where s is the length of a side. In this case, A = 36 cm^2, so s^2 = 36. Taking the square root of both sides, we get s = √36 = 6 cm.

Multiple choice

A triangular plot of land has sides of length 20 m, 25 m, and 30 m. What is its area?

  1. 275 m^2

  2. 300 m^2

  3. 325 m^2

  4. 350 m^2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of a triangle is given by the formula A = √s(s - a)(s - b)(s - c), where s is the semiperimeter and a, b, and c are the lengths of the sides. In this case, s = (20 + 25 + 30) / 2 = 37.5 m. Therefore, A = √37.5(37.5 - 20)(37.5 - 25)(37.5 - 30) = √37.5 * 17.5 * 12.5 * 7.5 = 300 m^2.

Multiple choice

Find the area of a parallelogram with base 12 cm and height 5 cm.

  1. 30 cm²

  2. 60 cm²

  3. 24 cm²

  4. 48 cm²
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area of a parallelogram = base * height = 12 cm * 5 cm = 60 cm²

Multiple choice

Determine the area of a trapezoid with bases 10 cm and 15 cm, and height 8 cm.

  1. 100 cm²

  2. 200 cm²

  3. 150 cm²

  4. 250 cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of a trapezoid = ((base1 + base2) / 2) * height = ((10 cm + 15 cm) / 2) * 8 cm = 100 cm²

Multiple choice

Calculate the area of a sector of a circle with radius 10 cm and central angle 60°.

  1. 30π cm²

  2. 60π cm²

  3. 15π cm²

  4. 45π cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of a sector = (π/360) * radius² * central angle = (π/360) * 10 cm² * 60° = 30π cm²

Multiple choice

Find the area of a segment of a circle with radius 12 cm and height 8 cm.

  1. 96π cm²

  2. 192π cm²

  3. 144π cm²

  4. 288π cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of a segment = (1/2) * (radius² - height²) = (1/2) * (12 cm² - 8 cm²) = 96π cm²