What is the area of the largest square that is inscribed in a semicircle of radius 10 cm?

Given:

The radius of the semicircle $r=10$ cm.

Concept Used:

The largest square inscribed in a semicircle will have one of its sides along the diameter of the semicircle, and the opposite two corners will touch the arc of the semicircle.

Area of square = $$a^2$$  

Pythagoras theorem;  

​$$\text{(Hypotenuse)}^2 = \text{(Perpendicular)}^2 + \text{(Base)}^2$$ ​

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