Answer:
168 ft.sq
Step-by-step explanation:
To calculate the surface area of this triangular prism we must break it into pieces :
Let's start with the triangles :
Let A be the area of one triangle :
- A = b*h*0.5 = 6*4*0.5 = 12 ft.sq
- 2A = 24 sq.ft
No need to calculate the area of each rectangle, we can multiply the sides of the triangle by the height :
we need the lenght of the third side
Let d be the third side :
- we can notice that the hight is passing through the midpoint of the 6 feet base and we can prove it with the pythagorian throrem but it's obvious
- now let's use the pythagorian theorem to calculate the "rd side :
- 3²+4²= d² ⇒ d²=25⇒ d=5
So the surface area Sa is :
Sa= 2A+ 9*(6+5+5) = 24 + 9*16 = 168 ft.sq
