Area Problems The sides of a triangular board are 13 meters, 14 meters and 15 meters. The cost of paining it at the rate of Rs. 8.75 per m 2 is? Rs. 722.50 Rs. 730.80 Rs. 735 Rs. 688.80 Rs. 722.50 Rs. 730.80 Rs. 735 Rs. 688.80 ANSWER EXPLANATION DOWNLOAD EXAMIANS APP s = (13 + 14 + 15 ) / 2 = 21, s-a = 8 , s-b = 7, s-c= 6? Area to be painted = ? [s(s-a) (s-b) (s-c)]=? [21 x 8 x 7 x 6] m2= 84 m2? Cost of painting = Rs. (84 x 8.75) = Rs. 735
Area Problems The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be: 20 cm 18 cm 41 cm 9 cm 20 cm 18 cm 41 cm 9 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 The length of each side of an equilateral triangle having an area of 4?3 cm 2 is? 4/?3 cm ?3/4 cm 4 cm 3 cm 4/?3 cm ?3/4 cm 4 cm 3 cm ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Area of equilateral triangle = ?3/4 a2 = 4?3.? a2 = 16? a = 4 cm
Area Problems The perimeter of an isosceles triangle is equal to 14 cm . The lateral side is to the base in the ratio 5 : 4 the area of the triangle is? 3/2?21 cm2 2?21 cm2 1/2?21 cm2 ?212 3/2?21 cm2 2?21 cm2 1/2?21 cm2 ?212 ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Let lateral side = (5y) cm and base = (4y) cm ? perimeter = 5y + 5y + 4y = 14 ?y = 1So, the sides are 5 cm , 5 cm and 4 cm Now s= 1/2 (5 + 5 + 4) cm = 7 cm (s-a) = 2 cm (s-b) = 2 cm and (s-c) = 3 cm? Required Area = ? (7 x 2 x 2 x 3) cm2=2?21 cm2
Area Problems An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is: 2.02% 4% 2% 4.04% 2.02% 4% 2% 4.04% ANSWER EXPLANATION DOWNLOAD EXAMIANS APP 100 cm is read as 102 cm. ∴ A1 = (100 x 100) cm2 and A2 (102 x 102) cm2. (A2 - A1) = [(102)2 - (100)2] = (102 + 100) x (102 - 100) = 404 cm2. ∴ Percentage error = ❨ 404 x 100 ❩% = 4.04%
Area Problems Angles of a quadrilateral are in the ratio 3 : 4 : 5 : 8. The smallest angle is 36° 40° 18° 54° 36° 40° 18° 54° ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Let First angle = 3kSecond angle = 4kThird angle = 5k and Fourth angle = 8kWe know 3k + 4k + 5k + 8k = 360°? 20k = 360° ? k = 18 °Measure of smallest angle = 3k =3 x 18 ° = 54 °
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