Answer:
V = 621.4 mm^3
Step-by-step explanation:
The volume of this pyramid is V = (1/3)(base area)(height). We must calculate the height from the info given. Draw in a vertical line to represent the height. Imagine a triangle with hypotenuse 12.8 mm (given) and shorter leg (13 mm)/2, or 6.5 mm.
The Pythagorean Theorem applies here: h^2 + (6.5 mm)^2 = (12.8 mm)^2. We get: h^2 + 42.25 = 163.84, or h^2 = 121.59, or h = √121.59, or
h = 11.03 mm.
Then, as before, the volume of this prism is V = (1/3)(base area)(height), or with specific numerical values V = (1/3)(13 mm)^2(11.03 m), or
V = 621.4 mm^3
