You built a skateboard ramp in the shape of a triangular prism. if you want to paint the entire ramp, even the bottom, what is the total area you will paint?

180 ft²

Step-by-step explanation:

In order to find the total area to paint, you need to find the surface area of the entire figure, which is the sum of the areas of all the sides.  Since there are 5 faces to the prism, including the bottom, you will need to add the area of all five faces.  The sides of the ramp are triangles with a base of 12 ft and height of 5ft.  The area of a triangle is: A = 1/2bh.  Since there are two triangles with the same dimensions:

12 x 5 = 60 ft²

Next, the top of the ramp is a rectangle with a length of 13 ft and width of 4 ft:

13 x 4 = 52 ft²

The bottom of the ramp is also a rectangle with length of 12 ft and width of 4 ft:

12 x 4 = 48 ft²

Lastly, the height of the ramp is 5 ft with a width of 4ft, also in the shape of a rectangle:

5 x 4 = 20 ft²

Add them all together:

20 + 48 + 52 + 60 = 180 ft²

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are