Question

Total surface area and volumeplease be as straightforward as possible thank you

Answer 1

Total surface area = 26.15 square units

Volume of the prism = 8.18 cubic units

Explanations:

The total surface area of the prism is the sum of the area of the surfaces.

To determine the slant height of the triangular base, we will use the sine rule as shown:

`\begin{gathered} (2)/(sin40)=(l)/(sin70) \\ l=(2sin70)/(sin40) \\ l=(1.8794)/(0.6428) \\ l=2.9 \end{gathered}`

Find the total surface area

`\begin{gathered} TSA=2(3*2)+(3*2.9)+(2\cdot2.9sin70^0) \\ TSA=12+8.7+5.45 \\ TSA=26.15units^2 \end{gathered}`

Find the volume of prism

`\begin{gathered} V=Base\text{ area}* height \\ V=(1)/(2)(2)(2.9)sin70^0*3 \\ V=2.9sin70^0*3 \\ V=8.18units^3 \end{gathered}`