Q. 21 A4.2( 6 Votes )

# D, E and F are mi A. 40 sq. cm

B. 8 sq. cm

C. 12 sq. cm

D. 100 sq. cm

Answer :

Given.

D, E and F are midpoints of sides BC, CA and AB respectively of a triangle ABC. If triangle ABC = 16 sq. cm

Formula used .

Median of triangle divides triangle in 2 equal parts

As F is midpoint of AB

CF is median of triangle ABC

∴ Area of triangle ABC = Area of triangle CFB + Area of triangle CFA

Area of triangle CFB = Area of triangle CFA=× Area of triangle ABC

Area of triangle CFB = Area of triangle CFA=8 cm^{2}

In triangle AFC

FE is acting as median

∴ Area of triangle CFA = Area of triangle CEF + Area of triangle AFE

Area of triangle CEF = Area of triangle AFE =× Area of triangle CFA

Area of triangle CEF = Area of triangle AFE=4 cm^{2}

Area of trapezium FBCE = Area of triangle ABC – Area of triangle AFE

= 16 cm^{2} – 4 cm^{2}

= 12 cm^{2}

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