Question

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answer 1

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