If GRAW is a square with side *a*, and triangle GMR is equilateral, then what is the area of triangle RAC (in terms of *a*)?

Area of △

By dropping a perpendicular (

*RAC*= ½*ah*By dropping a perpendicular (

*h*), from C to RA, we create two right triangles: △*RDC*and △*DAC*.△

Since GA bisects a right angle, this makes the angle DAC 45°. From there we can see that △

*DAC*Since GA bisects a right angle, this makes the angle DAC 45°. From there we can see that △

*DAC*is an isosceles triangle, and thus*DA*=*h*.△

Since △

*RAC*Since △

*GMR*is equilateral, it follows that all interior angles are 60°, which forces angle CRD to be 30°. Thus, △*RDC*is a 30°-60°-90° triangle and we can use our knowledge of trigonometric ratios to deduce that RD =*h*√3.Putting together this knowledge, we can say that:

*a*=

*RA*=

*RD*+

*DA*=

*h*√3 +

*h*=

*h*(√3 + 1)

So,

By substituting this back into Area of △

*RAC*= ½*ah*, we get:How about the area of △

*GCM*?