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$A B C$ is a triangle in which $D$ is a triangle in which is the midpoint of $B C$ is the midpoint of . $E$ . and $F$ and are mid-points of $D C$ are mid-points of and $A E$ and respectively. If area of $Δ A B C$ respectively. If area of is $16 cm 2$ is, then the area of $Δ D E F$ , then the area of from the following choices is:

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2 c m 2

4 c m 2

8 c m 2

16 c m 2

answer is A.

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Detailed Solution

It is given that,

A B C

is a triangle in which

D

is the midpoint of

B C

E

and

F

are mid-points of

D C

and

A E

respectively.
The area of

Δ A B C

16 cm 2

.
Draw the figure.
Question Image

Use median theorem which states that a median divides a triangle into

2

triangles of equal area.
For

Δ A B C,

A D

is the median.
Area of

Δ A D C = 12 × Area of Δ ABC

= 12 × 16

= 8 c m 2

Area of

Δ A D C = 8 c m 2

.
For

Δ A D C,

A E

is the median.
Area of

Δ A E D

= 12 × A r e a of Δ A D C

= 12 × (8)

Area of

Δ A E D = 4 c m 2

.
For

Δ A E D

D F

is the median.
Area of

Δ D E F = 12 × Area of Δ AED

= 2 cm 2

Area of

Δ D E F = 2 c m 2

.
Hence, option 1) is correct.

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