Q21 of 31 Page 232

D, E and F are midpoints of sides BC, CA and AB respectively of a triangle ABC. If triangle ABC = 16 sq. cm., then the area of the trapezium shaped region FBCE is

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 cm2


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 cm2


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


= 16 cm2 – 4 cm2


= 12 cm2

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