In the given figure AB||CD||EF at equal distancesand AF is a transversal. GH is perpendicular to AB. If AB=4.5cm,GH=4cm and FB=8cm find the area of ️GDF
Answers
Given : AB||CD||EF at equal distances and AF is a transversal. GH is perpendicular to AB.
AB=4.5cm,GH=4cm and FB=8cm
To Find : area of ️GDF
Solution:
Area of ΔABF = (1/2) * AB * BF
= (1/2) * 4.5 * 8
= 4.5 * 4
= 18 cm²
ΔGDF & ΔABF
∠A =∠G Corresponding angles
∠F = ∠F Common angles
ΔGDF ≈ ΔABF ( using AA)
Area of ΔGDF / Area of ΔABF = (DF / BF)²
=> Area of ΔGDF / 18 = (4/ 8)²
=> Area of ΔGDF / 18 = 1/4
=> Area of ΔGDF = 4.5 cm²
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