Question

Work out the area of triangle ABC?

Answer 1

`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`