Chapter SH, Problem 12.1MPS

i.

To determine

Write the bases, faces, edges and vertices of given solid.

  

Answer to Problem 12.1MPS

Solid has 2 bases, 5 faces, 9 edges and 6 vertices.

Explanation of Solution

Given:

  

Calculations:

Here, we have given triangular prism.

From figure,

There are two bases of triangular prism via ADE and BCF.

Triangular prism has five faces via ADE, BCF, ABFE, DCFE, ABCD.

There are 9 edges of triangular prism via AD, DE, AE, BC, BF, CF, EF, AB, DC.

Triangular prism has 6 vertices namely A, B, C, D, E, F.

Conclusion:

Therefore, we are able to show bases, faces, edges, vertices of triangular prism.

ii.

To determine

Calculate volume of the tent.

  

Answer to Problem 12.1MPS

Volume of the tent is $87.5f{t}^3$

Explanation of Solution

Given:

  

Calculations:

Here, we have given triangular prism.

We know that, volume of triangular prism is given as, $\frac{1}{2}\times Areaofcross\sec tion\times length$

Now putting values in the formula, we get volume of triangular prism.

  $\begin{array}{l}volumeoftriangularprism=\frac{1}{2}\times Areaofcross\sec tion\times length\\ =\frac{1}{2}\times 5\times 5\times 7\\ volumeoftriangularprism=87.5f{t}^3\end{array}$

Conclusion:

Therefore, we are able to calculate the volume of the tent.

iii.

To determine

Calculate the fabric required to make the tent.

  

Answer to Problem 12.1MPS

  $1122.6f{t}^2$ Fabric will require making tent.

Explanation of Solution

Given:

  

Calculations:

Here, we have to calculate how much fabric will be required to make a tent. For this we need surface area of triangular prism.

We know that, surface area of triangular prism is given as, $Base\times height+Perimeter\times heightofprism$

Now putting values in the formula, we get volume of triangular prism.

  $\begin{array}{l}Surfaceareaoftriangularprism=Base\times height+Perimeter\times heightofprism\\ =\left(5\times 5\right)+\left((5\times 5.6\times 5.6)\times 7\right)\\ =25+1097.6\\ Surfaceareaoftriangularprism=1122.6f{t}^2\end{array}$

Conclusion:

Therefore, we are able to calculate fabric required to make tent.