Answer:
A. The volume of the prism = 204.7 cm³
Step-by-step explanation:
The difficult part is finding the hight x in the triangle with sides 6 6 and 7.
The half of the base of this triangle = 3,5
So we have the right sided triangle with a hypothenusa of 6, one right side of 3,5 and one right side which is x (and is unknown).
Use Pythagoras to find the value of x.
x² + (3,5)² = 6²
x² = 6² - (3,5)²
x² = 36 - 12,25
x² = 23.75
x = +- SQRT(23.75)
{Only the positive part has a meaning.}
x = 4.873
So now it is easy.
The area of the triangle = 3.5 * x
with x = 4.873
The area of the triangle = 3.5 * 4.873
The area of the triangle = 17.06 cm²
The volume of the prism = 12 * the area of the triangle
The volume of the prism = 12 * 17.06
The volume of the prism = 204.67
rounded on 1 decimal.
The volume of the prism = 204.7 cm³
