Question : In the given figure, ABCD is a square of side 14 cm. E and F are mid-points of sides AB and DC respectively. EPF is a semi-circle whose diameter is EF. LMNO is square. What is the area (in cm2) of the shaded region?
Option 1: 108.5
Option 2: 94.5
Option 3: 70
Option 4: 120
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Correct Answer: 94.5
Solution : Given that ABCD is a square of side 14 cm. The area of the semicircle = $\frac{\pi r^2}{2}$ = $\frac{\pi (7)^2}{2}$ = 77 cm2 Since the radius of the semicircle is equal to the diagonal of a smaller square. The diagonal of a square = 7 cm The side of a smaller square = $\frac{7}{\sqrt2}$ cm The area of a smaller square = $\frac{49}{2}$ cm2 The area of a bigger square = 142 = 196 cm2 The area of the shaded region = The area of a bigger square – The area of a smaller square – The area of the semicircle The area of the shaded region = 196 – 77 – $\frac{49}{2}$ = 94.5 cm2 Hence, the correct answer is 94.5.
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Question : In the given figure, ABCD is a square. EFGH is a square formed by joining mid-points of sides of ABCD. LMNO is a square formed by joining mid-points of sides of EFGH. A circle is inscribed inside LMNO. If the area of a circle is 38.5 cm2 then what is the area (in cm2) of square ABCD?
Option 1: 98
Option 2: 196
Option 3: 122.5
Option 4: 171.5
Question : In a trapezium ABCD, AB and DC are parallel sides and $\angle ADC=90^\circ$. If AB = 15 cm, CD = 40 cm and diagonal AC = 41 cm, then the area of the trapezium ABCD is:
Option 1: 245 cm2
Option 2: 240 cm2
Option 3: 247.5 cm2
Option 4: 250 cm2
Question : A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is: (take $\pi=\frac{22}{7}$)
Option 1: 125 cm2
Option 2: 230 cm2
Option 3: 550 cm2
Option 4: 616 cm2
Question : In the given figure, the radius of a circle is $14\sqrt{2}$ cm. PQRS is a square. EFGH, ABCD, WXYZ, and LMNO are four identical squares. What is the total area (in cm2) of all the small squares?
Option 1: 31.36
Option 2: 125.44
Option 3: 62.72
Option 4: 156.8
Question : If the diameter of a sphere is 3.5 cm, then what is the total surface area of the sphere?
Option 1: 45.75 cm2
Option 2: 42.6 cm2
Option 3: 38.5 cm2
Option 4: 34.25 cm2
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