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? 18 cm2 12 cm 2 19 cm2 9 cm 2 18 cm2 12 cm 2 19 cm2 9 cm 2 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 Diagonals of a rhombus area 1 m and 1.5 m in lengths. The area of the rhombus is 0.75 m2 1.5 m2 0.375 m2 1.5 m2 0.75 m2 1.5 m2 0.375 m2 1.5 m2 ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Area of rhombus =(d1 x d2)/2 =(1 x 1.5)/2 m2= 0.75 m2
Area Problems Area of a square is 1/2 hectare. The diagonal of the square is? 50? 2 meter 250 meter 50 meter 100 meter 50? 2 meter 250 meter 50 meter 100 meter ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Area = 1/2 hectare = 10000 / 2 m2= 5000 m2Again Area = 1/2 x (Diagonal)2So 1/2 x (Diagonal)2 = 5000m2? Diagonal2= 10000 ? Diagonal = 100
Area Problems The area of circle inscribed in an equilateral triangle is 462 cm . The perimeter of the triangle is? 126 cms 42 ? 3 cms 168 cms 72.6 cms 126 cms 42 ? 3 cms 168 cms 72.6 cms ANSWER EXPLANATION DOWNLOAD EXAMIANS APP ? 22/7 x r2 = 462? r2 = (462 x 7) /22 = 147? r = 7?3 cm ? Height of the triangle = 3r = 21?3 cmNow, ? a2 = a2/4 + (3r)2? 3a2/4 = (21?3)2? a2 = (1323 x 4)/3? a = 21x 2 = 42 cm? Perimeter = 3a = 3 x 42=126 cm
Area Problems The ratio of the area of the circumcircle and the incircle of a square is 1 : 2 2 : 1 ?2 : 1 1 : ?2 1 : 2 2 : 1 ?2 : 1 1 : ?2 ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Ratio of the areas of the circumcircle and incircle of a square = [(Diagonal)2?] / [(Side)2?]= [(Side x ?2)2] / (Side)2 = 2/1 or 2 : 1
Area Problems The area of sector of a circle of radius 5 cm, formed by an arc of length 3.5 cm is? 8. 75 sq.cms 35 sq.cms 55 sq.cms 17.5 sq.cms 8. 75 sq.cms 35 sq.cms 55 sq.cms 17.5 sq.cms ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Area of sector = ( arc length x radius ) / 2 cm2= (3.5 x 5 ) / 2= 8.75 cm2
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