Discussion

Question:

In the figure given below, DE || BC = 1/3 of BC. If area of triangle ADE = 20 cm², then what is the area (in cm²) of triangle DEC?

Explanation:

Let us draw AF which is perpendicular to both DE and BC

∆ADE ≈ ∆ABC (since DE || BC)

⇒ AF : AG = DE : BC = 1 : 3

⇒ AF : FG = 1 : 2

For ∆ADE and ∆DEC
Base is same for both i.e., DE while height of ∆DEC which is FG is twice that of height of ∆ADE which is AF

∴ Area of ∆DEC will be twice that of ∆ADE

⇒ Area of ∆DEC = 2 × 20 = 40 cm².

Hence, option (a).

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