# Area- Aptitude Questions and Answers

 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? 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? 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) 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? 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