Area- Aptitude Questions and Answers

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The length and breadth of a rectangular hall are 40 m and 30 m respectively. What is the distance between two opposite corners of the hall?

A)
20 m

B)
35 m

C)
50 m

D)
40 m


Correct Answer :

50 m


Explanation :

Distance between two corners of hall
= √(Length2 + Breadth2)
= √(402 + 302) = √(1600 + 900) = 50 m

The area of the base of a rectangular tank is 6500 cm2 and volume of water contained in it is 2.6 m3. The depth of water (in metres) in the tank is

A)
2.5

B)
3

C)
4

D)
5.5


Correct Answer :

4


Explanation :

Let the depth of water be x m.Then
(6500/10000) * x = 2.6
x =(2.6*10000)/6500
= 4 m

The ratio of areas of two squares A and B are 4:25. If the side of the square A is 6m. Then, what is the measure of the side of square B?

A)
256m

B)
15m

C)
12m

D)
32m2


Correct Answer :

15m


Explanation :

area of square A= (6)²= 36 m²
let side of square B is x, So area of square B= x² m²

As given 36:x²:: 4:25
36/x² = 4/25
9/x² = 1/25
(3/x)²= (1/5)²
3/x = 1/5
x = 15 m
So side of square B has a length of 15 m

What is the measure of the base angle of an isosceles triangle, if its vertical angle is 70°?

A)
110°

B)
55°

C)
90°

D)
70°


Correct Answer :

55°


Explanation :

The sum of all the angles of a triangle must equal 180 degrees.
An isosceles triangle has two (Base) angles that are equal. The vertex angle is the odd one. So:

the measure of each base angle x.then
x + x + 70 = 180
2x = 180-70
x = 110/2
x = 55
The base angles measure 55°

If 'x' units are added to the length of the radius of a circle, what is the number of units by which the circumference of the circle is increased?

A)

X


B)


C)

2πX


D)

X2



Correct Answer :

2πX


Explanation :

Let the radius of the circle be r .
The circumference of the circle will therefore be 2 πr .

If the radius is increased by 'X' units, the new radius will be (r + X) .

The new circumference will be 2 π(r + X) = 2 πr + 2 πX
Hence, the circumference increases by 2 πX units.

The sides of a triangle are 30, 40 and 50 cm. Then this triangle is a?

A)

right-angled triangles


B)

acute-angled triangle


C)

obtuse-angled triangle


D)

equilateral triangle



Correct Answer :

right-angled triangles


Explanation :

As per Pythagoras Theorem, a triangle with a right angle (an angle of 90°) has a special relationship between the lengths of its three sides.
If the longest side (called the hypotenuse) is c and the other two sides (next to the right angle) are called a and b, then:
a2 + b2 = c2 Pythagoras' Theorem

Therefore, the triangles that follow this rule will be right angled triangles.

The triangle with sides 30, 40, 50 follows the Pythagorean theorem, so it is a right angle
302 + 402 = 900 + 1600 = 2500 = 502

Also 30, 40 and 50 are multiples of 3, 4, and 5 which is a well known "the 3-4-5 triangle"

3-4-5 triangle: there are some right-angled triangles, where all three sides are whole numbers called Pythagorean Triangles. And the three whole number side-lengths are called a Pythagorean triple or triad.

Below the list examples of Pythagorean triples-
3, 4, 5
5, 12, 13
6, 8, 10
7, 24, 25
8, 15, 17
9, 12, 15
9, 40, 41
10, 24, 26
12, 16, 20
12, 35, 37
14, 48, 50
15, 20, 25
15, 36, 39
16, 30, 34
18, 24, 30
20, 21, 29
21, 28, 35
24, 32, 40
27, 36, 45
30, 40, 50

A polygon has 44 diagonals, the number of its sides are?

A)

9


B)

10


C)

11


D)

12



Correct Answer :

11


Explanation :

Polygon: A polygon is a 2-dimensional shape that is formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons.

Let the side is n. because there are n sides, we have to subtract n from total number of line formed by joining two adjacent vertices of polygon.

number of diagonals = nC2 -n = n(n-1)/2 - n
number of diagonals = n(n-3) / 2 = 44
n2 - 3n - 88 = 0
(n+3) (n-11) = 0

n=11 (n can not be negative)
So the number of sides in a shape with 44 diagonals is 11.

If the length and breadth of a rectangular plot were increased by 20 percent; then what would be the percent increase in the area of the plot?

A)

20%


B)

44%


C)

26%


D)

36%



Correct Answer :

44%


Explanation :

Let the length of rectangle be x and breadth be y
So Area= length*breadth= x*y

According to The question
length = x + x*20/100= x *(1 + 1/5)=6x/5
breadth = y + y*20/100=y *(1 + 1/5)= 6y/5

New Area= 6x/5 × 6y/5 = 36*xy/25

Changes in area= 36*xy/25 - xy =xy* (36-25 / 25) =11*xy/25

% change = (11*xy / 25)*100 / xy = 44% area would be increase

If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle?

A)

40 cm


B)

50 cm


C)

60 cm


D)

30 cm



Correct Answer :

50 cm


Explanation :

Let x and y be the length and breadth respectively.
Area of rectangle = x*y
Area of square = (x-4) * (y+3)


As is given , (x-4) * (y+3)= x*y
3x – 4y = 12 ……………………………….(i)

for a square, length = width
(x-4) = (y+3)
x - y = 7 ……………………………….(ii)

Solving eq (i) & (ii) x= 16 and y = 9
Therefore perimeter of rectangle = 2(x+y)= 2(16+9)= 50 cm

If the ratio of areas of two square is 225:256, then the ratio of their perimeters is?

A)

256:225


B)

225:256


C)

16:15


D)

15:16



Correct Answer :

15:16


Explanation :

Let the side of squares be x and y respectively. Then
As is given ,
x2 / y2 = 225/256
x / y = (225/256) = 15 / 16

Ratio of their perimeters = 4x / 4y = x / y = 15 / 16

The circumference of the semi-circle is 180 cm. If the side of a square is 60% more than the diameter of the circle, what is the perimeter of the square?

A)

368 cm


B)

464 cm


C)

486 cm


D)

448 cm



Correct Answer :

448 cm


Explanation :

Given that circumference of semi circle is = 180
let the radius of this Semi circle be R
πR + 2R = 180
R(22/7 + 2)= 180
So, R =180*7 /36

Diameter of this semi circle, D = 2*R

Now, Side of the square = 160/100 D = 160/100 * 2R = 3.2*R

Perimeter of square = 4 * Side of the square = 4*3.2*R = 448

Which one of the following triples does not represent the sides of a triangle?

A)

(3, 4, 5)


B)

(4, 7, 10)


C)

(3, 6, 8)


D)

(2, 3, 6)



Correct Answer :

(2, 3, 6)


Explanation :

If a, b, c represents the sides of the triangle, then sum of the two sides must be greater than the third
side.
Since, 2 + 3 < 6
Hence, (2, 3, 6) can’t be side of a triangle.

If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is?

A)

6 cm


B)

5 cmm


C)

4.5 cm


D)

4 cm



Correct Answer :

4 cm


Explanation :

Let l and b the length and breadth of the rectangle respectively.
Now, according to the question 2(l + b) = 10
l + b = 5 …eq(i)
and lb = 4 …eq(ii)
From Eqs. (i) and (ii), we have
l(5 - l) = 4
5l - l2 = 4
l2 - 5l + 4 = 0
(l - 4)(l - 1) = 0

length, l = 4 or 1

The angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is?

A)

20º


B)

40º


C)

50º


D)

60º



Correct Answer :

40º


Explanation :

Since the angles of a triangle are in the ratio 2 : 4 : 3.

Smallest angle = (2/ 2+4+3)180°
= (2/9)180°
= 40°

A house site is in the shape of a square. Its area is 1225 sq metres. What is its perimeter?

A)

140 m


B)

160 m


C)

180 m


D)

200 m



Correct Answer :

140 m


Explanation :

Area of a square = 1225 m²
(side)² = 1225
side = √1225 = 35 m

Now, perimeter of a square = 4*side = 4*35
=140 m

The area of a square field is 7396 sq metres. Find its perimeter?

A)

300 m


B)

344 m


C)

388 m


D)

400 m



Correct Answer :

344 m


Explanation :

Area of a square = 7396 m²
(side)² = 7396
side = √7396 = 86 m

Now, perimeter of square = 4*side = 4*86
=344 m

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