Work out the area of triangle ABC?

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1 Answer
Jim G.
May 20, 2018

#10" cm"^2#

Explanation:

#"the area (A) of "triangleABC" is calculated using"#

#•color(white)(x)A=1/2bh#

#"where b is the base and h the perpendicular height"#

#"here "b=AC" and "h=BD#

#AC=3sqrt5+sqrt5=4sqrt5#

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

#triangleABD#

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

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

#color(white)(rArrBD)=sqrt((5sqrt2)^2-(3sqrt5)^2)#

#color(white)(rArrBD)=sqrt(50-45)=sqrt5#

#rArrA=1/2xx4sqrt5xxsqrt5=10" cm"^2#

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