In the figure, PQRS is a square of sides 8cm. What is the area of \(\bigtriangleup\)UVW?
Attached Figure / Diagram
A
64 sq. cm
B
40 sq.cm
C
50 sq.cm
D
10 sq.cm
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
In △ UQV
|UV|\(^2\) = 6\(^2\) + 4\(^2\) (Pythagora's theorem)
|UV| = \(\sqrt{52}\) = 7.21cm
Also, in △ WVR
|WV|\(^2\) = 2\(^2\) + 2\(^2\) = 4 + 4 = 8 (same reason as above)
|WV| = \(\sqrt{8}\) = 2.83
Therefore, the area of △ UVW = \(\frac{1}{2}\) x 2.83 x 7.21 = 10.21 ≈ 10cm\(^2\)
Source: Myschool Past Questions Archive (Record #32981)