9514 1404 393
Answer:
14.5 square units
Explanation:
There are several methods for finding the area of an acute scalene triangle with mostly irrational side lengths. Here's one.
Define X(4, 2) and Y(9, 2). The trapezoid XUTY has bases XU=9-2=7 and TY=6-2=4. Its height is XY=9-4=5, and its area is found from the formula ...
A = 1/2(b1 +b2)h
A = 1/2(7+4)(5) = 55/2 = 27.5
The area of our triangle is this trapezoid's area less the areas of triangles XUS and YTS. Those areas can be found from the formula ...
A = 1/2bh
∆XUS area = 1/2(2)(7) = 7
∆YTS area = 1/2(3)(4) = 6
So, the area of ∆STU is ...
area STU = area XUTY -area XUS -area YTS = 27.5 -7 -6
area STU = 14.5 . . . square units