A triangular prism has a base that is an isosceles right triangle with sides

11 ft, 11 ft, and 15.6 ft.The height of the prism is 15 ft.What is the surface area of this prism?Another triangular prism with height 15 ft has a base that is an isosceles triangle that is not a right triangle. The sides of the base measure 11 ft, 11 ft, and 12.1 ft.

The surface area of the prism with the isosceles right triangle base is _ ft^{2}.

Please fill in the blank.

Guest May 20, 2017

#1**0 **

The surface area of the prism with the isosceles right triangle base is \(685ft^2\).

The surface area of any prism can be calculated using the following formula:

Let S= Surface Area

Let L= Lateral Area (Area of everything but the base)

Let B= Area of one base

Let P= Perimeter of the base

Let H= height of prism

\(S=L+2B\)

\(L=PH\)

Okay, let's get started now that we have determined the formula. Let's start by solving for L, the lateral surface area.

P= perimeter of the base

\(P= (11+11+15.6)ft=37.6ft\)

\(H=15ft\)

To find the lateral surface area, multiply P by h.

\(L=PH=37.6ft*15ft=564ft^2\)

The only variable to find next is B, the area of a triangle is 1/2*bh. Because the base is a right isosceles triangle, the base and the height are both 11.

\(B=\frac{1}{2}bh=\frac{1}{2}*11*11=60.5ft^2\)

Remember, the formula requires us to find 2B:

\(2B=(2*60.5)ft^2=121ft^2\)

Now, plug L and 2B back into the formula to get the final answer:

\(S=L+2B\)

\(S=(564+121)ft^2=685ft^2\)

Normally, you would have to find the surface area of the other triangular prism, but the final answer only asked about the triangle with the right isosceles base, so there is no need to calculate the other one.

TheXSquaredFactor
May 20, 2017

#1**0 **

Best Answer

The surface area of the prism with the isosceles right triangle base is \(685ft^2\).

The surface area of any prism can be calculated using the following formula:

Let S= Surface Area

Let L= Lateral Area (Area of everything but the base)

Let B= Area of one base

Let P= Perimeter of the base

Let H= height of prism

\(S=L+2B\)

\(L=PH\)

Okay, let's get started now that we have determined the formula. Let's start by solving for L, the lateral surface area.

P= perimeter of the base

\(P= (11+11+15.6)ft=37.6ft\)

\(H=15ft\)

To find the lateral surface area, multiply P by h.

\(L=PH=37.6ft*15ft=564ft^2\)

The only variable to find next is B, the area of a triangle is 1/2*bh. Because the base is a right isosceles triangle, the base and the height are both 11.

\(B=\frac{1}{2}bh=\frac{1}{2}*11*11=60.5ft^2\)

Remember, the formula requires us to find 2B:

\(2B=(2*60.5)ft^2=121ft^2\)

Now, plug L and 2B back into the formula to get the final answer:

\(S=L+2B\)

\(S=(564+121)ft^2=685ft^2\)

Normally, you would have to find the surface area of the other triangular prism, but the final answer only asked about the triangle with the right isosceles base, so there is no need to calculate the other one.

TheXSquaredFactor
May 20, 2017

#2**0 **

Excellent explanation, Guest.....why don't you register and become a member???

We need more people like you on here!!!!

CPhill
May 20, 2017

#3**0 **

Well, I took your word, and I think TheXSquaredFactor is the perfect username!

TheXSquaredFactor
May 22, 2017