Area Aptitude Test Paper 731) One of the four angles of a rhombus is 90 degrees. If each side of the rhombus is 20 cm, what will be the length of the longer diagonal?
Answer: A Explanation: A rhombus with one of its angle 90 degrees is a square. So, both the diagonals are of equal length. Now, Diagonal of a square= √2 × side Given Side = 20 cm So, Diagonal = 20 √2 cm 32) What is the area of the largest circle that can be drawn inside a square of side 20 cm?
Answer: B Explanation: The diameter of the largest circle that can be drawn inside a square = length of the side of the square As per the question: The side of the square = 20 cm. So, radius of the circle = 20/2 = 10 cm Area of a circle = π × radius^{2} The area of the largest circle = π × 102 = 100 π cm^{2} 33) If the side of a square is equal to the diameter of a circle, what is the area of the square if the area of the circle is 81π sq. cm?
Answer: C Explanation: Area of the circle = 81π sq. cm. π × radius^{2} = 81π Radius = 9 cm Diameter of circle = 9 *2= 18 cm Now, Diameter of circle = Side of the square = 18 cm So, Area of the square = Side^{2} = 18^{2} = 324 sq. cm. 34) The perimeter of a circle and an equilateral triangle are equal. Find the area of the equilateral triangle if the area of the circle is 141π.
Answer: A Explanation: The perimeter of a circle and an equilateral triangle are equal: Let the length of each side of equilateral triangle = A As per the questions, the perimeters are equal. So, 2 π r = 3 A Area of circle is given = 141 π So, π r^{2} = 144 π r = 12 Thus, 2 π * 12 = 3 A A = 24 π /3 The area of a equilateral triangle = (√3/4) * side^{2} = (√3/4) * (24 π /3) ^{2} = (√3/4) * 8 π * 8 π = 0.43 * 25.12 * 25.12 = 271.34 sq. cm. 35) The diameter of a circle is increased by 100%. What is the percentage increase in area?
Answer: D Explanation: Let the diameter = d Original area = π * (d/2) ^{2} = π d^{2}/4 New Area = π * (2d/2) ^{2} = π (2d/2) (2d/2) = π d^{2} Increase in area = (π d^{2}  π d^{2}/4) = 3 π d^{2} / 4 Percentage increase = (increase in area/ original area) * 100 = (3 π d^{2} / 4) * (4/ π d^{2}) * 100 = 300 % Area Aptitude Test Paper 1 Area Aptitude Test Paper 2 Area Aptitude Test Paper 3 Area Aptitude Test Paper 4 Area Aptitude Test Paper 5 Area Aptitude Test Paper 6 Area Aptitude Test Paper 8 Area Concepts
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