Question

ce area of an object would be useful.
umingehicleshow all of your thinking.2.3volume:surface area:

Explanation:

Step1: Calculate the volume

The volume formula for a triangular prism is \(V = B\times h\), where \(B\) is the area of the triangular base and \(h\) is the height of the prism (the length along the direction perpendicular to the base).
The area of the triangular base \(B=\frac{1}{2}\times6\times8 = 24\) (using the formula for the area of a triangle \(A=\frac{1}{2}bh\), where \(b = 6\) and \(h = 8\)). The height of the prism \(h = 24\). Then \(V=24\times24=576\)

Step2: Calculate the surface area

The surface area of a triangular prism \(S=2B + P\times h\), where \(B\) is the area of the base, \(P\) is the perimeter of the base, and \(h\) is the height of the prism.
We know \(B = 24\), \(P=6 + 8+10=24\) (using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), \(6^{2}+8^{2}=36 + 64=100=10^{2}\) to confirm it's a right - triangle), and \(h = 24\). Then \(S=2\times24+24\times24=48 + 576=624\)

Answer:

Volume: \(576\)
Surface area: \(624\)