The area of a triangle is given by:
[tex]A=\frac{1}{2}bh[/tex]Where
A is the area
b is the base length
h is the height
We can clearly see that the height, h, is 17.
The base of the flag would be:
34 - (10 + 7)
= 34 - (17)
= 17
b = 17
Now, we can simply substitute and find out the answer:
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(17)(17) \\ A=\frac{1}{2}(289) \\ A=144.5 \end{gathered}[/tex]Answer