Answer:
The lateral surface area of a prism is the sum of the surface areas of the sides of the prism.
Since the bases of the prism are triangles, there are three sides. The area of each lateral is the product of a side of the triangle times the height of the prism.
We can express this as Lateral Surface Area LSA = (s1xh) + (s2xh) + (s3+h), where "s1, s2, s3" are the lengths of the sides of the triangle and "h" is the height of the prism.
We can factor out "h" to get LSA = hx(s1+s2+s3) where the factor "s1+s2+s3" is the perimeter of the triangle.
Solving for "h", we get h = LSA / (s1+s2+s3)
For your specific problem, h = 300 / (4 + 5 + 6) = 300 / 15 = 20
We have to calculate the suface of the four walls and the ceiling.
Surface of the four walls=2(10 ft * 10ft ) + 2(12 ft * 10 ft)=200 ft² + 240 ft²=
=440 ft²
Surface of the ceiling=10 ft * 12 ft=120 ft²
Total surface=440 ft² + 120 ft²=560 ft²
Now, we have to caluclate the number of gallons of paint.
1 gallon------------------------400 ft²
x----------------------------------560 ft²
x=(1 gallon * 560 ft²) / 400 ft²=1.4 gallons.
answer: Ryan need to paint all four walls and the ceiling 1.4 gallons.
