​ In the given figure AB//CD/EF at equal distances and AF is a transversal. GH is perpendicular to AB . If AB = 4.5 cm, GH = 4 ​

Question

In the given figure \(\overline{AB}|| \overline{CD} || \overline{EF}\) at equal distances and AF is a transversal. \(\overline{GH}\) is perpendicular to \(\overline{AB}\). If AB = 4.5 cm, GH = 4 cm and FB = 8 cm, find the area of ΔGDF.

Answer 1

In the given figure \(\overline{AB}|| \overline{CD} || \overline{EF}\) at equal distances.

\(\overline{AF}\) is a transversal and  \(\overline{GH}\) is perpendicular to \(\overline{AB}\)

So, GH = 4 cm, AB = 4.5 cm, FB = 8 cm 

To find area of ΔGDF, 

From ΔABF, D is mid point of \(\overline{BF}\)

Similarly ‘G’ is mid point of \(\overline{AF}\)

So BD ⊥ DF, AG = GF

Median divides a triangle into two equal triangles.

∴ Area of ΔABG = Area of ΔBGF

Similarly \(\overline{GD}\) is median of ΔBGF.

Area of ΔABG = 2 × area of ΔDGF

Area of ΔDFG = 1/2 area of ΔABG

Area of ΔABG = 1/2 × 4.5 × 4 = 9 sq.cm

Area of ΔDGE = 1/2 × 9 = 4.5 sq.cm