in the figure AE||DB, DA||BE and D is the midpoint of BC. if ar(triangle ADC)=12 squre cm find area of quadrilateral AEBC
Answers
Given : AE||DB, DA||BE and D is the midpoint of BC
ar(triangle ADC)=12 cm²
To find : area of quadrilateral AEBC
Solution:
AE||DB, DA||BE and D is the midpoint of BC.
Hence DC =BD = AE and ACDE and ADBE are parallelogram
in Parallelogram ACDE
Area of Δ ADE = Area of Δ ADC ( as diagonal divided parallelogram in two equal area triangle )
Similarly in Parallelogram ADBE
Area of Δ ADE = Area of Δ BDE
Area of Δ ADE = Area of Δ ADC = Area of Δ BDE = 12 cm²
area of quadrilateral AEBC
= Area of Δ ADE+ Area of Δ ADC + Area of Δ BDE
= 12 + 12 + 12
= 36 cm²
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