AB^2 + BC^2 = AC^2

AB^2 + 1 = 4

AB = root (3)

Area = 1 /2 AB* BC

= root ( 3) / 2

Ans : B

Rule: any triangle formed in the semicircle where diameter is one of triangle's sides; the triangle formed is a right angle triangle.

area of triangle = 1/2 * BC * AB

AC = diameter = hypotenuse

AC^2 = BC^2 + AB^2

AC = 2 r = 2 & BC = 1

2^2 = 1 + AB^2

4 - 1 = AB^2

AB = sqrt3


area = sqrt3/2


alternatively, if you know that triangle is a right triangle

with 90degree angle or hypotenuse= 2 , 30degree angle= 1 then 60degree will always be sqrt3

if you know the above rule, area can be found out within 20 seconds.

Hope this helps.

i should never take a practice test this at midnight again, i completely over looked the right triangle. arrgh!