MHB What is the area of triangle $STV$?

[anemone]

Hi all, I happened to see this primary 6 math geometry problem and thought it was a fun (not straightforward but not too hard) problem. Try it and post your solution if you are interested. (Cool)

In the figure, not drawn to scale, $UX=XY=YT$ and $UV=VS$. Given that the area of triangle $XVU$ is 14 cm$^2$, find the area of triangle $STV$.
[TIKZ]
\coordinate[label=left:U] (U) at (0,0);
\coordinate[label=right:T] (T) at (12, 0);
\coordinate[label=below: X] (X) at (4,0);
\coordinate[label=below: Y] (Y) at (8,0);
\coordinate[label=above: V] (V) at (2,1);
\coordinate[label=above:S] (S) at (4,2);
\coordinate[label=above: W] (W) at (7.2,0.4);
\draw (S) -- (U)-- (T)-- (S);
\draw (V) -- (X);
\draw (S) -- (Y);
\draw (V) -- (T);
[/TIKZ]

 

[kaliprasad]

Area of $\triangle STV$ = area of $\triangle UVT$

because they are on equal base and same base

now area of $\triangle UVT$ is 3 times area of $\triangle UVX$

as height is same and base is 3 times

so area of $\triangle STV$ = 3 * area of $\triangle UVX$ = $42cm^2$