Area- Aptitude Questions and Answers - in Hindi

Side of roumbus =52/4 = 13 cm

Area of the roumbus = (product of diagonals)/2

Let ABCD is rhombus, in which Side of roumbus =AB=13cm , BD=24cm and AC=? cm
the digonal of rhoumbus bisect each other at right angle

in the right angel AOB
OA²+OB²=AB²
OA²+(BD/2)²=AB²
OA²+(12)²=(13)²
OA²= (13)² - (12)²
OA = √(169-144) =√25 = 5
Hence the lenght of other dignoal is AC=2*OA= 2*5= 10cm
Thus,Area of the roumbus = (product of diagonals)/2
=> ( 24 * 10 ) /2 => 120 cm²

Let side = X cm
then Area = length of a side² ⇒ (X)² cm²

increased side by 30 then, new side = 130 % of X ⇒ (130/100) *X ⇒ 1.3X cm
And,new area = length of a side² ⇒ (1.3)² sq. cm

Increase in area = (1.3*X)² - (X)² cm²
= 1.69*X² - X²
= .69*X²
% Increase = 69

Let 2a = 3b = 4c = x
So, a = x/2 b = x/3 c = x/4
The L.C.M of 2, 3 and 4 is 12
Therefore, a : b : c = x/2 × 12 : x/3 × 12 : x/4 = 12
= 6x : 4x : 3x
= 6 : 4 : 3
Therefore, a : b : c = 6 : 4 : 3

the perimeter of a triangle is sum of its side
Lets take a variable x for the sides,
hence the sides will be 6x,4x,3x respectively.

Perimeter = 6x+4x+3x
208 = 6x+4x+3x = 13x
13x = 208
=> x = 208/13
x=16

Length of the longest side = 6x = 6 x 16 = 96.

let Length =L and Width=W

Perimeter = 2(L + W) = 70
L + W = 35
L = 35 - W

Area = WL = 276
W(35 - W) = 276
35W - W² = 276
0 = W² - 35W + 276
0 = (W - 23)(W - 12)
W = {12, 23}
L = {23, 12}

Therefore, the sides of the rectangle are 23 and 12
The longest side of the rectangle is 23 units.

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

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

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

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°

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.

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

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.

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