Dr Fiendish tells his p*g, Freddy, to mow the northeast side of the lawn(blue). However , Freddy accidentally mows the southwest side(yellow). What is the difference (in units squared) between the part Freddy has mowed and the part he should mow?
+23252 Assuming that the blue triangle is a right triangle:
-- using the Pythagorean Theorem, we get the missing side to be 5
-- the area will be: ½·5·12 = 30
The yellow triangle is a 30-60-90 triangle, so:
-- the side opposite the 30o angle is 13/2
-- the side adjacent to the 30o angle is (13/2)·sqrt(3)
-- the area will be: ½·( 13/2 )·[ (13/2)·sqrt(3) ] = (169/8)·sqrt(3)
The difference in area is: | 30 - (169/8)·sqrt(3) |
