Question

Please help me and explain!

Answer 1

Answer:

453.5 in²

Step-by-step explanation:

The given composite figure consists of a triangular prism and a rectangular prism.

The total surface area is equal to the sum of the surface areas of both the figures excluding the area of the base of triangular prism.

Total surface area of rectangular prism is given as:

$S_1=2(lw+wh+lh)$

The length of the rectangular prism is, $l=16\ in$

The width of the rectangular prism is, $w=7\ in$

The height of the rectangular prism is, $h=3\ in$

Therefore, $S_1=2(16\times 7+7\times 3+3\times 16)=362\ in^2$

Now, area of triangular prism consists of 3 rectangular faces and 1 triangular face. The base triangle is not included in the surface area.

So, surface area of the triangular prism is the sum of the areas of these faces.

$S_2=6\times 6+3\times 6+5\times 6+\frac{1}{2}\times 5\times 3\\S_2=36+18+30+7.5\\S_2=91.5\ in^2$

Therefore, the total surface area of the composite figure is given as:

$S_T=S_1+S_2\\S_T=362+91.5=453.5\ in^2$