Q. 34.6( 28 Votes )

Find the area of

Answer :

area of trapezium ABCD = area of rectangle ADCE + area(ΔBEC)…(i)


let us find area of rectangle ADCE


length = AD = 8 cm


breadth = AE = 3 cm


area of rectangle = length × breadth


area of rectangle ADCE = length × breadth


= AD × AE


= 8 × 3


= 24 sq. cm


Therefore, area of rectangle ADCE = 24 sq. cm


From figure EC || AD


BEC = EAD = 90° …corresponding angles


BEC = 90°


And since ADCE is a rectangle EC = AD


EC = 8 cm


Now let us find area(ΔBEC)


area of triangle = × base × height


area(ΔBEC) = × EC × BE


area(ΔBEC) = × 8 × 3


area(ΔBEC) = 4 × 3


area(ΔBEC) = 12 cm2


From (i)


area of trapezium ABCD = area of rectangle ADCE + area(ΔBEC)…(i)


= 24 + 12


= 36 sq. cm


therefore, area of trapezium ABCD = 36 sq. cm


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