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 maths introduction to three dimensional geometry distance between two points in 3d distance between two points in space scalars and vectors

If the extremities of a diagonal of a square are $(1, -2, 3)$ and $(2, -3, 5)$, then area of the square is

  1. $6$
  2. $3$
  3. $\displaystyle \dfrac{3}{2}$
  4. $\sqrt{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the extremities of the diagonal of a square be $(1,-2,3)$ and $B(2,-3,5)$.
Then $AB$ is given by $ {({1}^{2} + {1}^{2} + {2}^{2})}^{0.5} $ = $ \sqrt{6} $
Hence, length of the side $ = \sqrt {3} $
So, area of square will be $ \sqrt{3} \times \sqrt{3}  = 3$

Multiple choice maths introduction to three dimensional geometry distance between two points in 3d distance between two points in space scalars and vectors

If the extremities of a diagonal of a square are $(1, -2, 3)$ and $(4, 2, 3)$ then the area of the square is

  1. $25$
  2. $50$
  3. $\displaystyle \frac{25}{2}$
  4. $\sqrt{50}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If $a$ is the length of a side of square then the length of diagonal is given by $\sqrt{2}a$. Distance between two given  points is $\sqrt{(1-4)^2+(-2-2)^2+(3-3)^2}=5=\sqrt{2}a$. Hence the area is given by $a^2=\dfrac{25}{2}$.

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

The area of square $ABCD$ is three-fourths the area of parallelogram $EFGH$. The area of parallelogram $EFGH$ is one-third the area of trapezoid $IJKL$. If square $ABCD$ has an area of $125$ square feet, calculate the area of trapezoid $IJKL$, in square feet.

  1. $75$
  2. $225$
  3. $350$
  4. $500$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given, area of square $ABCD$ is three fourth of area of parallelogram $EFGH$,

And the area of parallelogram $EFGH$ is one-third of the area of trapezoid $IJKL$ and area of square $ABCD$ is $125$.
Let the area of trapezoid $IJKL$ is $x$
Then  area of  parallelogram $EFGH =$ $\dfrac{1}{3}x$
And  area of square $ABCD=$ $\dfrac{3}{4}$ area of  parallelogram $EFGH=$ $\dfrac{3}{4}\times \dfrac{1}{3}x=\dfrac{1}{4}x$
But area of square $ABCD =125$
$\therefore \dfrac{1}{4}x=125$
$\Rightarrow x=500$
So, area of trapezoid $IJKL=500$.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

The area of a field in the shape of a trapezium measures $1440{m}^{2}$. The perpendicular distance between its parallel sides is $24m$. If the ratio of the parallel sides is $5:3$, the length of the longer parallel side is:

  1. $45m$
  2. $60m$
  3. $75m$
  4. $120m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Parallel sides $= 5x,\, 3x$
area $=\dfrac{24}{2}(5x+3x)=1440 $
$12(8x)=1440$
$x=\dfrac{120}{8}=15$ 
$5x=15\times 5$ 
     $=75m$
Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

If area $(\Delta ABC)=36 cm^2, area (\Delta DEF)=64 cm^2$ and $DE=6.4 cm$. Find AB if $\Delta ABC\sim \Delta DEF$

  1. $3.6$ cm
  2. $7.2$ cm
  3. $4.8 $cm

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In similar triangles, $\dfrac {area\Delta ABC}{area \Delta DEF}=\dfrac {AB^2}{DE^2}=\dfrac {36}{64}$


$\Rightarrow \dfrac {AB}{6.4}=\dfrac {3}{4}\Rightarrow AB=4.8$.

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Area of a square is $(100\pm 2)m^2$. Its side is:

  1. $(10\pm 1)m$
  2. $(10\pm 0.1)m$
  3. $(10\pm \sqrt 2)m$
  4. $10\pm \sqrt 2$ %
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Area=(Length)^2$
$Length =(Area)^{1/2}$
             $=(100\pm 2)^{1/2}$
             $=(100)^{1/2}\pm \dfrac {1}{2}\times 2$
             $=(10\pm 1)m$

Multiple choice maths geometry similarity and right angled triangle angle theorems for a right angled triangle apollonius's theorem

Find the side of the square whose diagonal is $16 \sqrt 2$ cm.

  1. $4$ cm
  2. $16$ cm
  3. $8$ cm
  4. $16\sqrt 2$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know that,

1) All angles of a square are congruent. i.e $90^o$
2) Diagonal of a square bisects each of its angles.
Therefore, the square gets divided into $2$ triangles of degrees $45^o-45^o-90^o$
$\therefore \sin 45^o = \cfrac {\text {side}}{\text {hyp}}$ 
$\therefore \cfrac {1}{\sqrt 2} = \cfrac {\text {side}}{16 \sqrt 2}$
$\therefore$ side of the square $= 16$ cm.

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

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.