What is the area formula for a half circle?

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Answer 1 · 2015-12-25T02:47:51

$\frac{π r^{2}}{2}$ $(pir^2)/2$

The typical area for a circle is:

$s s s A = π r^{2}$ $color(white)(sss)A=pir^2$

Divide both sides by $2$ $2$ , or multiply both by $\frac{1}{2}$ $1/2$ , to find the formula for half the area:

$s s s \frac{A}{2} = \frac{π r^{2}}{2}$ $color(white)(sss)A/2=(pir^2)/2$

We can do a practice problem: what's the area of a half a circle (a semicircle) with a radius of $6$ $6$ ?

$s s s A_{semicircle} = \frac{π {(6)}^{2}}{2}$ $color(white)(sss)A_"semicircle"=(pi(6)^2)/2$

$s s s \Rightarrow \frac{36 π}{2}$ $color(white)(sss)=>(36pi)/2$

$s s s \Rightarrow 18 π$ $color(white)(sss)=>18pi$