9514 1404 393
Answer:
(a) 10.2 ft
Step-by-step explanation:
The total surface area S is the sum of the base area and the lateral area. The base area is the area of the two triangular bases, which have a "base" of 6 ft and a height of 4 ft.
area of 2 bases = 2(1/2)bh = bh = (6 ft)(4 ft) = 24 ft²
The lateral surface area is the sum of the areas of the three rectangular faces. That will be ...
total face area = (4 ft)(x) +(6 ft)(x) +(7.2 ft)(x) = (17.2 ft)(x)
So, the total surface area is ...
200 ft² = 24 ft² + (17.2 ft)(x)
176 ft² = (17.2 ft)x . . . . . . . . . . subtract 24 ft²
(176 ft²)/(17.2 ft) = x ≈ 10.2 ft . . . . . divide by the coefficient of x
The unknown prism height is about 10.2 ft.
