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 cm^{2}

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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