Work out the area of triangle ABC?

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1 Answer
Jim G.
Apr 17, 2018

#"area "=4" units"^2#

Explanation:

#"area of "triangleABC=1/2xx"base"xx"height"#

#color(white)(xxxxxxxxxxxx)=1/2xxACxxBD#

#triangleABD" is a right triangle"#

#"using "color(blue)"Pythagoras' theorem"#

#AB^2=AD^2+BD^2#

#rArrBD=sqrt(AB^2-AD^2)#

#color(white)(rArrBD)=sqrt((2sqrt5)^2-(3sqrt2)^2)#

#color(white)(rArrBD)=sqrt(20-18)=sqrt2#

#rArr"area of "triangleABC=1/2xx4sqrt2xxsqrt2#

#color(white)(xxxxxxxxxxxxxx)=2xx2=4" units"^2#

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