ΔPED is similar to ΔGFP Ratio of area = 9:16 Therefore ratio of sides =
√9
16
=3:4 Hence, P divides GD in the ratio 3 : 4. ΔAGD=(
7
3
)2×9=49sq.cm [ΔAGD similar to ΔFGP] So area of AEPF = 49 - [16 + 9] = 24 sq. cm Similarly area of BFI = (
10
3
)2×9=100sq.cm Therefore area of BHPG = 100 - (49 + 9) = 42 sq. cm Similiarty area of PDCI = (
11
7
)2×49−49−16 = 56 sq.cm Area of triangle ABC = (9 + 16 + 49 + 24 + 42 + 56) = 196 sq. cm
Alternative method: Ratio of the corresponding sides is 3:4:7 since the areas are in the ratio 9:16:49 and all the triangles are similar. Hence GP + PD = BH+IC = HI. So HI is half of BC. Since triangle 3 is similar to Triangle ABC and HI is thecorresponding Side to BC . and is half of it the area of triangle 3 must be 1/4 the area of triangle ABC So area of triangle ABC = 196 sq cm.