Question

What is the lateral surface area of the prism and the total surface area of the prism round to the nearest 10th if needed ?I just need a brief explanation With the answer

Answer 1

step 1

Find out the lateral surface area of the triangular prism

The lateral area is the area of the three rectangular faces

`LA=P*H`

where

P is the perimeter of the triangular face

H is the height of the prism

H=9.5 mm

`\begin{gathered} P=10.5+7.5+11 \\ P=29\text{ mm} \end{gathered}`

substitute

`\begin{gathered} LA=29*9.5 \\ LA=275.5\text{ mm}^2 \end{gathered}`

The lateral area is 275.5 square millimeters

step 2

Find out the surface total area

The surface area is equal to the lateral area plus two times the area of the triangular face

`SA=LA+2B`

where

B is the area of the triangular face

`B=(1)/(2)*b*h`

where

b=10.5 mm

h=6 mm

substitute

`\begin{gathered} B=(1)/(2)*10.5*6 \\ B=31.5\text{ mm}^2 \end{gathered}`

substitute in the formula of surface area

`\begin{gathered} SA=275.5+2*31.5 \\ SA=338.5\text{ mm}^2 \end{gathered}`

The surface area is 338.5 square millimeters