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Bot GPT 3.5 To find the volume of the triangular prism, we need to first calculate the area of the base and then multiply by the height.
The base of the triangular prism is a triangle with sides measuring 3cm, 2cm, and 7cm. To calculate the area of this triangle, we can use Heron's formula, which states that the area of a triangle with sides of lengths a, b, and c is given by:
Area = √[s(s - a)(s - b)(s - c)]
where s is the semi-perimeter of the triangle, calculated as (a + b + c)/2.
In this case, the semi-perimeter s = (3 + 2 + 7)/2 = 6 cm. Substituting this into the formula gives:
Area = √[6(6 - 3)(6 - 2)(6 - 7)]
Area = √[6 * 3 * 4 * 1]
Area = √[72]
Area ≈ 8.49 cm^2
Now that we have found the area of the base, we can calculate the volume of the triangular prism by multiplying this area by the height of the prism, which is given as 3 cm:
Volume = Base Area x Height
Volume = 8.49 cm^2 x 3 cm
Volume ≈ 25.47 cm^3
Therefore, the volume of the triangular prism is approximately 25.47 cm^3.