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प्रश्न
In the adjoining figure, a trapezium ABCD is shown in which AB || DC then, ar (ΔAOD) is equal to:
पर्याय
ar (ΔOCD)
ar (ΔAOB)
ar (ΔBCD)
ar (ΔBOC)
MCQ
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उत्तर
ar (ΔBOC)
Explanation:
With AB || DC, the triangles AOB and COD are similar, alternate interior angles and vertical angles.
So, `(AO)/(OC) = (BO)/(OD)`.
The area of ΔAOD = `1/2` × AO × OD × sin θ and the area of ΔBOC = `1/2` × BO × OC × sin θ, where θ is the vertical angle between the two diagonal segments.
Hence, `("area" (AOD))/("area" (BOC))`
= `(AO xx OD)/(BO xx OC)`
= 1
So, area (AOD) = area (BOC).
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