Question

medians of cf and be of a ∆ abc intersect at g. if area of quadrilateral afge is 36 cm² then area of ∆gbc is​

Answer 1

area (△FBC) = 1/2 area (△ABC)        .....(i)

[ Median divides the triangle into two triangles of equal area ]

area (△EBC) = 1/2 area (△ABC)     ......(ii)

From equation (i) and (ii),

                 area (△FBC) = area (△EBC)

Subtract area (△BGC) from both sides

     area(△FBC) - area(△BGC) = area (△EBC) - area (△BGC)

therefore,                area(△FGB) = area (△EGC)                       ....(iii)

                            area(△ABE) = area (△BEC)            [Since, BE is median]

area(△BFG) + area (Quadrilateral AFGE) = area (△BGC) + area (△GEC)

⇒                   area (Quadrilateral AFGE) = area (△BGC)     [ From equation (iii)]