A square is drawn inside a semicircle of radius 10 cm so that one whole side of the square lies along the diameter and its two upper corners touch the arc. Find the area of the square in cm².

Question

Accepted Answer

80. Put the centre of the diameter at the origin and let the side be s. The upper corners are at (±s/2, s) and lie on the arc, so (s/2)² + s² = 10². That gives (5/4)s² = 100, so s² = 80. The area of the square is s² = 80 cm².

A square is drawn inside a semicircle of radius 10 cm so that one whole side of the square lies along the diameter and its two upper corners touch the arc. Find the area of the square in $cm^{2}$ .

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More Areas & Volumes practice

A square is drawn inside a semicircle of radius 10 cm so that one whole side of the square lies along the diameter and its two upper corners touch the arc. Find the area of the square in cm2.

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Areas & Volumes practice

A square is drawn inside a semicircle of radius 10 cm so that one whole side of the square lies along the diameter and its two upper corners touch the arc. Find the area of the square in $cm^{2}$ .