Answer:
(a) 66 cm³
Explanation:
You want the volume of a right triangular prism with a base right triangle that has a leg length of 3 cm and a hypotenuse of 5 cm. The height of the prism is 11 cm.
Base
The base triangle is a 3-4-5 right triangle, so will have an area of ...
A = (1/2)bh
A = (1/2)(4 cm)(3 cm) = 6 cm²
Volume
The volume of the prism is ...
V = Bh . . . . . where B is the base area
V = (6 cm²)(11 cm) = 66 cm³
The volume of the prism is 66 cubic centimeters.
__
Additional comment
As you can see, the "work" is greatly simplified by the recognition of the {3, 4, 5} right triangle. If you must use the Pythagorean theorem to find the missing side length, you will find it to be ...
b = √(c² -a²) = √(5² -3²) = √16 = 4
The answer can be estimated by realizing the missing dimension is less than 5. The volume of a rectangular prism of side lengths 3, 5, and 11 would be 3·5·11 = 165 cm³. A triangular prism with the same overall dimensions would have 1/2 that volume, or 82.5 cm³. Since the prism shown has a side length less than 5, its volume will be smaller than 82.5 cm³. The only reasonable answer is 66 cm³.
#95141404393