# Area- Aptitude Questions and Answers

 The areas of two circular fields are in the ratio 16 : 49. If the radius of the bigger field is 14 m, then what is the radius of the smaller field? A) 4 m B) 8 m C) 9 m D) 10 m Correct Answer : 8 m Explanation :Let r1 and r2 be the radius of the circles. Area of circle = πr2 As is given, Ratio of area πr12/πr22 = 16/49 r12 / r22 = 16 / 49 r1 / r2 = 4 / 7 r1 = (4/7) * 14 ( r2 = 14 m) r1 = 8 m If each of the dimensions of a rectangle is increased by 200%, the area is increased by? A) 300% B) 400% C) 600% D) 800% Correct Answer : 800% Explanation :Let the length and width of the rectangle are x and y respectively. Then, area of rectangle = xy Now, Length and Width of rectangle after increasing by 200% So, New Length = x + (200/100)x = 3x New Width = y + (200/100)y = 3y New area = 3x*3y = 9xy Percentage increase in area = (9xy-xy)*100 / xy = 800 % A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent in the form of a circle, it encloses an area equal to? A) 121 cm2 B) 144 cm2 C) 154 cm2 D) 168 cm2 Correct Answer : 154 cm2 Explanation :As is given, area of square = a2 = 121 cm2 So, side of square, a = 11 cm length of the wire = Perimeter of square of side a = 4a = 4*11 = 44cm Let the radius of circle be r cm. Then, Perimeter of circle = Length of wire => 2πr = 44 cm => r = 44/2π = 7 (π = 22/7) Now, Area of circle = πr2 = (22/7) *7*7 = 154 cm2 If the area of a square is 16 cm2, then the area of the square joining the mid-points of the sides is? A) 32 cm2 B) 8 cm2 C) 4 cm2 D) 16 cm2 Correct Answer : 8 cm2 Explanation :Area of square, b² = 16 cm² side of square, b = √16 =4 cm Diagonal of square inside the big square = Side of big square √2s = b = 4 s = 2√2 cm The area of the small square = 2√2 * 2√2 = 4*2 = 8cm² The area of a triangle is 150 m2 . The ratio of its base to its height is 3:4. Find the length of its base ? A) 45 cm B) 30 cm C) 15 cm D) 10 cm Correct Answer : 15 cm Explanation :Let the base and height be 3x & 4x. Area of triangle = 1/2 × Base × Height 150 = 1/2 × 3x × 4x x = 5 Hence the length of the base is 15 cm.