Step-by-step explanation:
the volume of a regular prism is simply
base area × height
in our case we have a triangular prism, which means the base area (as well as the top area) is a triangle.
the base is defined as a 45° - 45° - 90° triangle.
so, since we have a 90° angle, this is a right-angled triangle.
the other 2 angles are equal to each other, so, it is an isoceles triangle (both legs are equally long).
since one leg is 8 in long, this means the other leg is 8 in too.
the area of a triangle is
baseline × height / 2
in case of a right-angled triangle (the legs enclose the 90° angle) one leg can be considered as the baseline, and the other leg as the height.
and the area is
leg1 × leg2 / 2
and in case of an isoceles right-angled triangle this is
leg² / 2
in our case
8² / 2 = 64/2 = 32 in²
now, the volume of the prism here is then
32 × 3.5 = 112 in³
