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In the given figure, ABCD is a trapezium in which AB || CD. If area of △BEC is 12 cm2, then area of △EDC is :

In the given figure, ABCD is a trapezium in which AB || CD. If area of △BEC is 12 cm<sup>2</sup>, then area of △EDC is. ARC Properties of Circle, R.S. Aggarwal Mathematics Solutions ICSE Class 9.

  1. 12 cm2

  2. 6 cm2

  3. 24 cm2

  4. none of these

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Answer

Since, AB || DC.

∴ Triangles BEC and EDC lie between the same parallel lines.

Both triangles have the same height (distance between AB and CD).

There bases are also equal:

Base of △BEC = EB = 6 cm

Base of △EDC = DC = 6 cm

We know that,

Area of triangle = 12\dfrac{1}{2} × base × height

Since both triangles (△BEC and △EDC) have same height and base.

So, there areas are also equal.

∴ Area of △BEC = Area of △EDC = 12 cm2.

Hence, option 1 is the correct option.

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