In a ΔABC if D and E are mid-points of BC and AD respectively such that ar (ΔAEC) = 4cm², then ar (ΔBEC) =

(a) 4 cm²

(b) 6 cm²

(c) 8 cm²

(d) 12 cm²

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Solution

Given: In ΔABC

(1) D is the midpoint of BC

(2) E is the midpoint of AD

(3) ar (ΔAEC) = 4 cm²

To find: ar (ΔBEC)

Calculation: We know that”the median of the triangle divides the triangle into two triangle of equal area”

Since AD is the median of ΔABC,

ar (ΔABD) = ar (ΔADC) …… (1)

EC is the median of ΔADC,

ar (ΔAEC) = ar (ΔDEC) …… (2)

⇒ ar (ΔDEC) = 4 cm²

EC is the median of ΔBED

ar (ΔBED) = ar (ΔDEC) …… (3)

From 2 and 3 we get,

ar (ΔBED) = ar (ΔAEC) …… (4)

⇒ ar (ΔBED) = 4 cm²

Now,

Hence the correct answer is option (c).

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In a ΔABC if D and E are mid-points of BC and AD respectively such that ar (ΔAEC) = 4cm2, then ar (ΔBEC) = (a) 4 cm2 (b) 6 cm2 (c) 8 cm2 (d) 12 cm2

In a ΔABC if D and E are mid-points of BC and AD respectively such that ar (ΔAEC) = 4cm², then ar (ΔBEC) =

(a) 4 cm²

(b) 6 cm²

(c) 8 cm²

(d) 12 cm²