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Find the area of a cyclic quadrilateral with sides 2, 2, 3, 1.

 Jan 11, 2020
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Find the area of a cyclic quadrilateral with sides 2, 2, 3, 1.

 

Formula: \(\boxed{ A = \sqrt{(s-a)(s-b)(s-c)(s-d)}\\ \text{where }s \text{ is the semiperimeter }\\s=\dfrac{a+b+c+d}{2} } \)

 

\(\begin{array}{|rcll|} \hline s &=&\dfrac{2+2+3+1}{2} \\ \mathbf{s} &=& \mathbf{4} \\ \hline \end{array} \)

 

\(\begin{array}{|rcll|} \hline A &=& \sqrt{(4-2)(4-2)(4-3)(4-1)} \\ A &=& \sqrt{2*2*1*3} \\ \mathbf{A} &=& \mathbf{2\sqrt{3}} \\ \hline \end{array}\)

 

 

laugh

 Jan 11, 2020

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