Area Problems The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be: 9 cm 41 cm 18 cm 20 cm 9 cm 41 cm 18 cm 20 cm ANSWER EXPLANATION DOWNLOAD EXAMIANS APP √l2 + b2 = √41. Also, lb = 20. (l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81 ⟹ (l + b) = 9. ∴ Perimeter = 2(l + b) = 18 cm
Area Problems If the radius of a circle be reduced by 50%. Its area is reduced by? 31.5% 65.5% 34.5% 39.5% 31.5% 65.5% 34.5% 39.5% ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Original area = ? x (r/2)2 = ?r2/4Reduction in area = ? r2 - 3? r2/4? Reduction per cent = [ 3?r2/4 x 4/(?r2) x 100 ] %= 75%
Area Problems If D,E and F are respectively the midpoint of the sides BC , CA and AB of a ? ABC and the area of ? ABC = 36m 2. Then area of ? DEF is? 12 cm 2 18 cm2 9 cm 2 19 cm2 12 cm 2 18 cm2 9 cm 2 19 cm2 ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Area of a triangle formed by joining the mid point of the sides of the triangle is 1/4th of area of the original triangle .So area of ? DEF = 36/ 4 = 9 m2
Area Problems The radius of the wheel of a vehicle is 70 cm. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle is? 31.68 km/hr. 36.25 km/hr. 32.72 km/hr. 29.46 km/hr. 31.68 km/hr. 36.25 km/hr. 32.72 km/hr. 29.46 km/hr. ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Circumference = 2?r = 2 x (22 / 7) x 70 cm = 440 cm Distance travelled in 10 revolutions = 440 x 10 cm = 4400 cm = 44 m? Speed = distance / time= 44 / 5 m/sec= (44 / 5) x (18 / 5) km/hr = 31.68 km/hr
Area Problems The Number of rounds that a wheel of diameter 7/11 m will make in going 4 km, is? 1700 1000 2000 1500 1700 1000 2000 1500 ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Number of round = total distance / circumference of wheel.= (4 x 1000) / ?d= (4 x 1000) / ( 22/7 x 7/11) = 2000
Area Problems The area of the sector of a circle, whose radius is 12 meters and whose angle at the centre is 42, is? 26.4 sq. meters 79.2 sq. meters 52.8 sq. meters 39.6 sq. meters 26.4 sq. meters 79.2 sq. meters 52.8 sq. meters 39.6 sq. meters ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Area of the sector = [(22/7) x 12 x 12] x [42°/360°] m2 = 52.8 m2
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