The solid prism has constant cross section which is a trianle sides 8cm, 7cm and 7cm long respectively. If the lenght of the prism is 9cm, calculate the volume of the prism.

Recall that the area of a prism is just area of the base times height. In this case, the base is the triangle. Since the lengths of side of triangle are given, we use Heron's formula to get first the area:

A = √(s(s-a)(s-b)(s-c))
where
a, b & c = lengths of side of triangle
s = half of the perimeter = 1/2*(a+b+c)
Substituting,
s = 1/2*(7+7+8)
s = 1/2*(22)
s = 11
A = √(s(s-a)(s-b)(s-c))
A = √(11(11-7)(11-7)(11-8))
A = √(11(4)(4)(3))
A = √(528)
A = 4√(33) = 22.98 cm^2

Finally, we multiply this to the height of the cylinder to get the volume:
V = A*h
V = 22.98*9
V = 206.8 cm^3

Hope this helps~ :)

To calculate the volume of a solid prism, you need to multiply the area of its cross-section with its length. In this case, the cross-section is a triangle with sides measuring 8cm, 7cm, and 7cm.

To find the area of a triangle, you can use Heron's formula. Heron's formula states that the area (A) of a triangle with sides a, b, and c is given by the following equation:

A = √(s(s - a)(s - b)(s - c))

where s is the semi-perimeter (half of the perimeter) of the triangle, calculated as:

s = (a + b + c) / 2

First, let's calculate the semi-perimeter of the triangle:

s = (8 + 7 + 7) / 2 = 11

Now, let's substitute the values into Heron's formula to find the area (A) of the triangle:

A = √(11(11 - 8)(11 - 7)(11 - 7))
= √(11 * 3 * 4 * 4)
= √(11 * 48)
= √528
≈ 22.98 cm²

Now that we have the area of the triangle cross-section, we can calculate the volume of the prism by multiplying it with the length:

Volume = Area × Length
= 22.98 cm² × 9 cm
≈ 206.82 cm³

Therefore, the volume of the prism is approximately 206.82 cm³.