If the angles of a triangle are `30^0a n d45^0` and the included side is `(sqrt(3)+1)c m` then the area of the triangle is______.

Explanation

Traiangle with given specification is drawn in the following figure.

To find area of the triangle ABC, we need to find the length of altitude AD.
Now, in triangle ADC,
`tan30^(@)=h/(CD)`
`rArr CD=h cot30^(@)=sqrt3h`
In triangle ADB,
`tan45^(@)=h/(BD)`
`rArr BD=h cot 45^(@)=h`
Now, `Bc=BD+DC`
`:. h=sqrt3h=sqrt3+1`
`:. h=1`
`:. " Area of triangle "ABC=1/2xxADxxBC=(sqrt3+1)/2 cm^2`