Are You Smart Enough To Solve This In 7 Seconds?

These are three squares with given areas. Find the shaded area.

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Solution

We can find the area of the two right-angled triangles adjacent to the middle square by first finding their individual bases.

For the right-angled triangle on the right, the base equals

For the right-angled triangle on the left, the base equals

We will now find the areas of the two triangles.

The triangle on the right has area

The triangle on the left has area

We will now label the diagram as follows

Consider the triangle with angle a, its area equals

Now consider the triangle with angle b, its area equals

But we know that

That means, the area of the shaded triangle with angle a equals

We also know that

Therefore, the area of the shaded triangle has the same area as the unshaded triangle.

By applying similar reasoning to the right-hand side, we get the shaded area

And that’s our answer. How amazing. Hey, don’t forget to clap👏 the article as a token of appreciation. Thank you 🦁

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