A geometry problem by Saimir Sulaj

Geometry Level 3

Above shows a unit square $ABCD$ such that both semi-circles passing through the centre of the square, $O$ . Find the area of the shaded region. Answer to 3 significant figures.

The answer is 0.143.

1 solution

Saimir Sulaj
Nov 16, 2015

Let "M" be the midpoint of "C" and "D". $\overline { MD }$ = 0.5 . First we find the area of the quarter-circle, which is $\frac { \pi { r }^{ 2 } }{ 4 }$ . Then, we subtract the area of triangle MOD. Lastly, we multiply this by 2. The final equation is: $\left( \left( \frac { \pi { (0.5) }^{ 2 } }{ 4 } \right) -\left( \frac { { 0.5 }^{ 2 } }{ 2 } \right) \right) \ast 2$

Moderator note:

Good clear explanation of how to obtain the area of the composite figure.

I followed this way 1) 4*area of 1 semicircle=x 2)area of the square-x (i.e)= 1-x lets keep that 1-x=y 3) finally y/4 yields the area of the shaded region.

Joseph Vincent - 5 years, 6 months ago

A geometry problem by Saimir Sulaj

The answer is 0.143.

1 solution

Moderator note:

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