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 maths construction of quadrilaterals trapeziums and kites quadrilaterals and their properties closed figures

The area of a trapezium is $24{ cm }^{ 2 }$. The distance between its parallel sides is $4 cm$. If one of the parallel sides is $7 cm$. What is the measure of the other parallel side ?

  1. $5 cm$
  2. $8 cm$
  3. $12 cm$
  4. $7 cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given that,


The area of the trapezium $A = 24c{m^2}$
Height $h = 4cm$

One of the side $a = 7cm$
Let the other side be $x$

SInce,
$A = \dfrac{1}{2} \times \left( {a + x} \right) \times h$
$24 = \dfrac{1}{2} \times \left( {7 + x} \right) \times 4$

$\dfrac{{24}}{2} = 7 + x$

$12 - 7 = x$

$x = 5$

Hence , the other side be the $5 \,cm$

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

The length of the parallel sides of a trapezium are 14 cm and 7 cm. If the length of third side is 8 cm and of fourth sides is c xm, then the number of possible integral value of x is :

  1. 12

  2. 13

  3. 14

  4. 17
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By the triangle inequality and the properties of a trapezium, the possible integral values for the fourth side x are constrained by the lengths of the parallel sides.

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

In trapezium PQRS, PQ($23$cm) and RS($13$ cm) are the bases. Find the area of the trapezium if the diagonals bisect angles SPQ and PQR.

  1. $350$ $cm^2$
  2. $276$ $cm^2$
  3. $216$ $cm^2$
  4. $410$ $cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If the diagonals bisect the base angles of a trapezium, the non-parallel sides are equal to the segments of the base. With bases 23 and 13, the non-parallel sides are 13 each. The height can be calculated using the Pythagorean theorem, and then the area is found.

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

The area of a trapezium is  $385 { cm } ^ { 2 } .$  Its parallel sides are in the ratio  $3 : 4$  and the perpendicular distance between them is  $11 { cm } .$  Its longer side is

  1. $35 cm$
  2. $30 cm$
  3. $40 cm$
  4. $60 cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the parallel sides be 3x and 4x. The area of a trapezium is given by (1/2) * (sum of parallel sides) * height. Thus, 385 = (1/2) * (3x + 4x) * 11. Solving this yields 385 = (7x / 2) * 11, so 385 = 38.5x, which means x = 10. The longer side is 4x = 4 * 10 = 40 cm.

Multiple choice

Which of the following quadrilaterals has the largest area?

  1. Rectangle

  2. Square

  3. Rhombus

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

A square has the largest area among all quadrilaterals with the same perimeter.

Multiple choice

Which of these formulas is NOT found in the Sulba Sutra?

  1. Area of a square = side^2

  2. Area of a rectangle = length * width

  3. Area of a circle = πr^2

  4. Area of a triangle = (1/2) * base * height
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The formula for the area of a circle (πr^2) is not found in the Sulba Sutra. The Sulba Sutra provides formulas for calculating the areas of squares, rectangles, and triangles, but not circles.

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

A farmer has 100 acres of land. He plants corn on 40% of the land, soybeans on 30% of the land, and wheat on the remaining land. How many acres of land does he plant corn on?

  1. 40

  2. 48

  3. 54

  4. 60
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The farmer plants corn on 40% of the land, which is 0.4 * 100 = 40 acres.

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

A farmer has 100 acres of land. He plants corn on 40% of the land, soybeans on 30% of the land, and wheat on the rest of the land. How many acres of land does he plant wheat on?

  1. 20

  2. 30

  3. 40

  4. 50
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The farmer plants corn on 40% of the land, which is 40% of 100 acres = 40 acres. He plants soybeans on 30% of the land, which is 30% of 100 acres = 30 acres. Therefore, he plants wheat on 100 acres - 40 acres - 30 acres = 30 acres.

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.