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$P$ is any point on base $B C$ is any point on base of $Δ A B C$ of and $D$ and is the mid-point of $B C$ is the mid-point of . $D E$ . is drawn parallel to $P A$ is drawn parallel to to meet $A C$ to meet at $E$ at . If $a r (Δ A B C) = 12 c m 2$ . If , then the area of $Δ P E C$ , then the area of is:

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6 cm 2

12 cm 2

18 cm 2

24 cm 2

answer is A.

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Detailed Solution

Given that,

P

is any point on base

B C

Δ A B C

and

D

is the mid-point of

B C

D E

is drawn parallel to

P A

to meet

A C

E

Since

A P ∥ E D

, we know that the area of the triangles between the same parallel and on the same base are equal. So,

Area (APE) = Area (APD) Area (APM) + Area (AME) = Area (APM) + Area(PMD) Area(AME) = Area(PMD) ......................... (1)

Calculate the area of triangle

A D C

.
Since median divides triangles into

2

equal parts.

Area (ADC) = 12 × Area (ABC) = 122 = 6 cm 2

Add the area of

M D C E

and area of

Δ A M E

Area (ADC) = Area (MDCE) + Area (AME) = Area (MDCE) + Area (PMD) [by(1)]

Area

(ADC) =

Area

(PEC)

So, area of triangle PEC is

6 c m 2

.
Therefore, area

P E C = 6 c m 2

.
Hence, option 1) is correct.

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