find the surface area of the rectangular triangular prism with height 35.5 yards, base 41 yards, length 35.5 yards

Question

Height of prism is 35.5 yards

Base is 41 yards

Length is 35.5 yards

Answer 1

All you need to do is add up the areas of the two triangles and the three rectangles

 

triangles 

 

Area of a Triangle=(Base)(Height)/2

 

A=(41)(35.5)/2

A=727.75

 

There's two triangles so you have to multiply that by two.

 

Total Area of triangles 1455.5 = 727.75 x 2

 

Now for the three rectangles:

 

Area of a Rectangle=(Base)(Height)

 

A=(35.5)(41)

A=1455.5

 

Now you multiple the Area times 3 for number of rectangles.

 

1455.5 x 3 = 4366.5

 

Then you add the total area of the two triangles and the three rectangles.

 

4366.5 + 1455.5 = 5822 ft^2

 

So, the total surface area  of the rectangular triangular prism is 5822 ft^2

 

Answer 2

The surface area, SA, is the total area, A, of the faces of a certain figure.  Since we have a rectangular triangular prism (not to be confused with a pyramid), the bottom of the figure is a rectangular shape.  The sides of the figure are shaped as a triangle. Think of this figure as a triangle with a large thickness.  We will have three rectangular faces  (one is the bottom base, and the other two are the sides), and two triangular faces.  I just wish that I could draw a picture for you.

 

A_{bottom base} = Length × Width

        = 41 yd × 35.5 yd

        = 1455.50 yd²

 

2 (A_{trianglaur sides})= 2 (base × height) / 2

           = 2 (41 yd × 35.5 yd) / 2

           = 1455.50 yd²

 

We need to find the missing side of the two other side faces.  These sides share the same side as the hypotenuse of the triangle.  The height is perpendicular to the base of the triangle.  This makes the triangle a right triangle.  We can use the Pythagorean theorem to find the missing side.

 

s = √(41/2)² + (35.5)²)

s = √(420.25 + 1260.25)

s = 40.99 yd

 

2 (A_{rectangular sides}) =  2(40.99 yd × 35.5 yd)

                        = 2910.29 yd²

 

 

Next is to add up all of the areas that were found and you will have your surface area.