# Area- Aptitude Questions and Answers - in Hindi

 One diagonal and perimeter of a rhombus are 24 cm and 52 cm respectively. The area of rhombus will be? A) 60 cm2 B) 120 cm2 C) 100 cm2 D) 30 cm2 Correct Answer :120 cm2 Explanation : 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 ABCD is a square of side X cm. Its side is increased by 30%. What is the change in its area? ABCD एक वर्ग है जिसकी भुजा 'X' सेमी हे। यदि इसकी एक भुजा 30% की वृद्धि कर दे तो इसके क्षेत्र में क्या परिवर्तन होगा? A) 60% B) 62.5% C) 63% D) 69% Correct Answer :69% Explanation :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 The sides of a triangle a, b, c are such that 2a = 3b = 4c and its perimeter is 208 cm. What is the length of the longest side? A) 48cm B) 96cm C) 64cm D) 54cm Correct Answer :96cm Explanation :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. What is the longest side of a rectangle which has a perimeter of 70 units and an area of 276 square units? A) 12 units B) 18 units C) 23 units D) 36 units Correct Answer :23 units Explanation :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. 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? दो वर्गो A और B के क्षेत्रों का अनुपात 4:25 है। यदि वर्ग A की भुजा 6 मीटर है। फिर, वर्ग B की भुजा का माप क्या होगा? 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°? एक समाद्विबाहु त्रिभुज के आधार कोण का माप क्या है, यदि उसका शिर्षकोण 70 डिग्री है? 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? यदि किसी वृत्त की त्रिज्या की लंबाई में 'X' इकाइयाँ जोड़ी जाती हैं, तो वृत्त की परिधि मे कितनी इकाइयाँ बढ़ जाती है? A) X B) 2π 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? एक त्रिभुज की भुजाएँ 30, 40 और 50 सेमी हैं। फिर यह त्रिभुज है? A) right-angled triangles /समकोण त्रिभुज B) acute-angled triangle /न्यून कोण त्रिभुज C) obtuse-angled triangle /अधिक कोण त्रिभुज D) equilateral triangle /समभुज त्रिभुज 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? एक बहुभुज में 44 विकर्ण है, तो उसकी भुजाओं की संख्या होगी? 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? यदि एक आयताकार भूखंड की लंबाई और चौड़ाई में 20 प्रतिशत की वृद्धि हुई थी; तो फिर भूखंड के क्षेत्र में प्रतिशत वृद्धि क्या होगी? 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