ad =1 and dc=1 ,ab=bc =ac polygon, angle A=105 degrees angle D is right angle, whats area?

ad =1 and dc=1 ,ab=bc =ac polygon, angle A=105 degrees angle D is right angle, whats area?
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1 Answer

AC is perpendicular to BD and the quadrilateral is a kite.

AC=√(DC²+AD²)=√2=AB=BC. CX=AX=√2/2=XD.

BC²=CX²+BX², so BX²=2-½=3/2, BX=√(3/2)=√6/2.

Area ABC=2×area of BCX=BX×CX=√12/4=2√3/4=√3/2.

Area ACD=CX×XD=½.

Total area ABCD=(1+√3)/2=1.366 approx.

by Top Rated User (1.1m points)

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