Solution to Adjacent Triangles

Triangle for the challenge.

This time, we wanted to find the area of the left triangle on the left, given that the area of the one on the right has area √2. First, let’s remember that the area of any triangle, say △xyz, has area xy*yz*sin(∠xyz)*0.5. Now, we can use this formula’s inverse to find the length of ad, which will be 1. And then, we can use this to find the area of △abd, which is 0.75. ∴ the area of △abd is 0.75.

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