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Geometry Level 1

In the above image, A B C D ABCD is a rectangle and E F C D EFCD is a parallelogram.

If A D : A B = 1 : 3 AD : AB = 1 : 3 , A E : E B = 1 : 3 AE : EB = 1 : 3 , and the area of A B C D ABCD is 10, what is the area of E F C D EFCD ?

10 8 9 11

Chung Kevin by Chung Kevin , 45, Australia

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5 solutions

If 2 figures have same base and lie between same parallels then the figures have equal area

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Raushan Sharma
Feb 18, 2015

Parallelograms on the same base and between the same parallels are equal in area.

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Henrique Ribeiro
Feb 16, 2015

The triangles DAE and CBF are congruent, so it's easy to see that putting DAE in CBF, the area will be the same, because the base is the same. If I remember, there is a Euclidean proposition about this.

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What do you mean that the figures are congruent? I don't think ABCD and EFCD are congruent, or similar.

Chung Kevin - 6 years, 3 months ago

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Can you see that if you keep the base, and pass the triangle DAE to CBF is the same area?

Henrique Ribeiro - 6 years, 3 months ago

Nothing is congruent here....... What are you talking about?? Are you talking about triangles AED and BFC?

Raushan Sharma - 6 years, 3 months ago

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Yes, you cannot see that triangle DAE = CBF?

Henrique Ribeiro - 6 years, 3 months ago

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I think you should specify that in your solution since it is a little confusing.

Alex Wang - 6 years, 3 months ago

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@Alex Wang – Yes, I'll edit it.

Henrique Ribeiro - 6 years, 3 months ago

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@Henrique Ribeiro – Thanks for adding that explanation. It makes your solution much easier to understand!

Chung Kevin - 6 years, 3 months ago
Jake Lai
Feb 16, 2015

A simple application of Cavalieri's principle.

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Isn't Cavalieri's Principle applicable for Solid objects and that too concerning their volume ?

A Former Brilliant Member - 6 years, 3 months ago

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Yes, but not exclusively.

Jake Lai - 6 years, 3 months ago

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Oh, ok . It means that I have to do a bit of light reading on that topic .

A Former Brilliant Member - 6 years, 3 months ago

For both the base and height is the same. Therefore areas are same.

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