The volume of a prism can be calculated using the following formula, where B is the area of the base and h is the height.
V=Bh
Let's first calculate the area of the base B. We can see that the base is a right triangle, so we can use the known formula to find its area.
B = 1/2 ab
However, we only know that a=9cm. To find b, we can use the Pythagorean Theorem.
a^2+b^2=c^2
We can see that the length of one of the legs is a = 9cm and the length of the hypotenuse is c = 15cm. We can use this information to find the length of b.
Since a negative side length does not make sense, we only need to consider positive solutions. Therefore, the length of the second arm of our triangle is b = 12cm. Finally, we can calculate the area of our prism's base.
