Basic area? but how to solve?

Geometry Level 3

There is a figure below (a rectangle). You can see different colors depicting different regions of the figure. The labels on the top of a region defines the area of that region.

Can you find the area of the green shaded region labelled with a question mark?

5.25 6 5.75 6.25 5.5 5 4.5 4.75

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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2 solutions

Syed Hamza Khalid
Sep 24, 2017

This problem can be solved with similar triangles property.

The White triangle is similar to the Red one Now Ratio of sides is 2:3 (as ratio of areas = ratio of based if the height is same)

Seeking that, White triangle = 9/4 * Yellow triangle = 9/2

Following all the above, the Green region: 5.5 u n i t s \large \color{#20A900}5.5\ units

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Kartik Jay
Sep 24, 2017

From the Law of sines; 4 A B C = sin ⁡ 45 C \frac{4}{ABC}=\frac{\sin 45}{C} \ ⇒ B = 4 5 5 \Rightarrow B=\frac{4\sqrt{5}}{5} \ Also by the same rule we get, \text{Also by the same rule we get,} \ E = 6 5 5 E=\frac{6\sqrt{5}}{5} \ solving these equations by similarity and area-ratio theorem we get the area of the white triangle as 4.5 \text{solving these equations by similarity and area-ratio theorem we get the area of the white triangle as 4.5} \ ⇒ A g r e e n = 5.5 \Rightarrow A_{green}=5.5 \

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