Question

You want to wrap a gift shaped like the regular triangular prism shown. How many square inches of wrapping paper do you need to completely cover the prism?You need ___ square inches of wrapping paper to cover the gift.(Round to the nearest whole number as needed.)

Answer 1

Step-by-step explanation:

Given;

We are given a triangular prism with the dimensions shown as indicated.

Required;

We are required to calculate the total surface area of the prism.

(This represents the total area of the gift wrapper needed to cover the gift shaped like a triangular prism)

Step-by-step solution;

We shall first take a look at the formula used to calculate the area of a triangular prism;

`TSA=(Perimeter* length)+(2* base\text{ }area)`

In order to determine the perimeter of the triangular face, we will need to calculate the slant height, since we already have the base length and the perpendicular height.

We shall use the Pythagoras' theorem to calculate the length of the side of the triangle as follows;

`\begin{gathered} c^2=a^2+b^2 \\ Where: \\ c=hypotenuse \\ a,b=other\text{ }sides \end{gathered}`
`\begin{gathered} 8.7^2=5^2+x^2 \\ \\ 75.69=25+x^2 \\ \\ 75.69-25=x^2 \\ \\ 50.69=x^2 \end{gathered}`

We now take the square root of both sides;

`\begin{gathered} √(50.69)=x \\ \\ 7.12=x \\ Rounded\text{ }to\text{ }the\text{ }nearest\text{ }whole\text{ }number: \\ x=7 \end{gathered}`

We can now re-label the triangle as follows;

We can now apply the formula as follows;

`TSA=(Perimeter* length)+(2* base\text{ }area)`
`TSA=(\lbrace7.1+7.1+10\rbrace*12)+(2*(1)/(2)\lbrace10*8.7\rbrace)`
`TSA=(24.2*12)+(87)=377.4`
`TSA=377.4`

Rounded to the nearest whole number, we now have;

ANSWER:

`Total\text{ }surface\text{ }area=377in^2`