In the attached figure, ST=5cm & QR=9cm. The area of the larger triangle is 50 sq.cm. What is the area of the black region?
Thanks,
Ron
Honestly I don't understand why you want to know the height of the triangle QRP because you already know that the area of the this triangle is 50 cm².
But: Since you know that $\displaystyle \overline{QR} = 9\ cm$ you can use the value of the area and the length of the base to calculate the length of the height:
$\displaystyle 50 =\frac12 \cdot 9 \cdot h~\implies~ h= \frac{100}9$
And now?