In the given figure, if AD = 3, DE = 4, AB = 12, BF = 2, FG = 6, BC = 10, then the value of M/N is:
(Assume : M is the area of the quadrilateral FGDE and N is the area of the triangle ABC.)
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 31/60.
| Understanding | Application |
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M = Area of queadrilateral FGDE = Area of triangle DBG - Area of triangle EBF Area of triangle = (1/2) x Multiple of adjacent sides x sin ( Angle between those sides) BE= AB - AD - DE |
Area of triangle EBF = (1/2) x BE x BF x sinB = (1/2) x 5 x 2 x sinB = 5 x sinB Area of triangle ABC = (1/2) x 12 x 10 x sinB = 60 x sinB M = Area of queadrilateral FGDE = Area of triangle DBG - Area of triangle EBF = 36 sinB - 5sinB = 31 sinB M/N = Area of queadrilateral FGDE / Area of triangle ABC = 31 sinB/60 sinB = 31/60 |