Area Aptitude Test Paper 7
31) 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?
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?
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 × radius2
The area of the largest circle = π × 102 = 100 π cm2
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?
Area of the circle = 81π sq. cm.
π × radius2 = 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 = Side2 = 182 = 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.
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 r2 = 144 π
r = 12
Thus, 2 π * 12 = 3 A
A = 24 π /3
The area of a equilateral triangle = (√3/4) * side2
= (√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?
Let the diameter = d
Original area = π * (d/2) 2 = π d2/4
New Area = π * (2d/2) 2
= π (2d/2) (2d/2)
= π d2
Increase in area = (π d2 - π d2/4) = 3 π d2 / 4
Percentage increase = (increase in area/ original area) * 100
= (3 π d2 / 4) * (4/ π d2) * 100
= 300 %
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