Surface area of a prism
Initial explanation
We find the surface area of the prism by finding the area of each part of the shown net and then adding them.
We have that
the surface area is given by the addition of the area of the 5 parts:
area 1 + area 2 + area 3 + area 4 + area 5
Finding the areas of each part
Area 1: rectangle
We know that the area of a rectangle is given by:
side 1 x side 2
In this case
side 1 = 6 ft
side 2 = 4 ft
Then, the area is
side 1 x side 2 = 6 ft x 4 ft
= 24 ft²
area 1 = 24 ft²
Area 2: rectangle
Since the sides of the second rectangle have the same measures as the first, then its area is the same:
area 2 = 24 ft²
Area 3: rectangle
As before, it is the same as the first area:
area 3 = 24 ft²
Area 4: triangle
We have that the area of a triangle is given by its base and its height. In this case the triangle is rotated
The area of a triangle is
(base x height)/2
In this case
base = 4 ft
height = 3.46 ft
then
(base x height)/2 = (4 ft x 3.46 ft)/2
= 6.92 ft²
Then
area 4 = 6.92 ft²
Area 5: triangle
Since the sides of this triangle have the same measures as the previous, then its area is the same:
area 5 = 6.92 ft²
Total area
The surface area is given by
area 1 + area 2 + area 3 + area 4 + area 5
= 24 ft² + 24 ft² + 24 ft² + 6.92 ft² + 6.92 ft²
= 3(24 ft²) + 2(6.92 ft²)
= 72 ft² + 13.84 ft²
= 85.84 ft²
Answer- the surface area of the fabric is 85.84 ft²