Answer:
[tex]A = \frac{h\sqrt{t^{2} - h^{2}}}{2}[/tex]
Step-by-step explanation:
Right triangle:
height h, width w, hypotenuse h
Area is: [tex]A = \frac{h*w}{2}[/tex]
Pytagoras theorem: [tex]h^{2} + w^{2} = t^{2}[/tex]
In this question:
To find the area, in terms of h and t, we have to write w as a function of h and t. So
[tex]h^{2} + w^{2} = t^{2}[/tex]
[tex]w^{2} = t^{2} - h^{2}[/tex]
[tex]w = \sqrt{t^{2} - h^{2}}[/tex]
So the area is:
[tex]A = \frac{h*w}{2}[/tex]
[tex]A = \frac{h\sqrt{t^{2} - h^{2}}}{2}[/tex]
