Answer:
The total surface area = 582 ft²
Explanation:
To find the surface area of it count the number of faces at first
The figure has 8 faces each 2 are equal
1- Two faces with dimensions 4 ft and 15 ft ( base and shaded face)
2- Two faces with dimensions 9 ft and 4 ft
3- Two faces with dimensions 4 ft and 6 ft
4- Two faces with dimensions 15 ft , 9 ft and 6 ft
Area of (1-) = 2(4 × 15) = 120 ft²
Area of (2-) = 2(4 × 9) = 72 ft²
Area of (3-) = 2(4 × 6) = 48 ft²
Area of (4-) = 2[(9 × 9) + (6 × 15)] = 2[81 + 90] = 2 × 171 = 342 ft²
∴ The total surface area = 120 + 72 + 48 + 342 = 582 ft²