MCQ

In a Δ*ABC* if *D* and *E* are mid-points of *BC* and *AD* respectively such that ar (Δ*AEC*) = 4cm^{2}, then ar (Δ*BEC*) =

#### Options

4 cm

^{2}6 cm

^{2}8 cm

^{2}12 cm

^{2}

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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 cm^{2}

**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 cm^{2}

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 cm^{2}

Now,

ar (ΔBEC) = ar (ΔBED) + ar (ΔDEC)

= 4 + 4 (subsituting the values)

ar(ΔBEC) = 8 cm^{2}

Concept: Concept of Area

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