Answer:
The surface area of the solid = 582 feet²
Explanation:
* At first lets study the solid
- it consists of 8 faces
- One base with dimensions 15 and 4 feet (1)
- Two side faces L-shaped with dimensions 15 , 4 , 9 ad 6 feet (2)
- One side face with dimensions 4 and 15 feet (3)
- One side face with dimensions 9 and 4 feet (4)
- One side face with dimensions 6 and 4 feet (5)
- One top base with dimensions 9 and 4 feet (6)
- One top base with dimensions 6 and 4 feet (7)
* Now lets find the area of the faces
- A(1) = 15 × 4 = 60 feet² ⇒ rectangular face
* We can find the area of L-shaped by this way
∵ Area of the square face = 15 × 15 = 225 feet²
∵ Area of the small rectangle = 9 × (15 - 9) = 54 feet²
- Lets subtract the area of the small rectangle from the area of
the square, to find the area of the L-shaped
- A(2) = 2 ( 225 - 54) = 2 (171) = 342 feet²
- A(3) = 4 × 15 = 60 feet² ⇒ rectangular face
- A(4) = 9 × 4 = 36 feet² ⇒ rectangular face
- A(5) = 6 × 4 = 24 feet² ⇒ rectangular face
- A(6) = 9 × 4 = 36 feet² ⇒ rectangular face
- A(7) = 6 × 4 = 24 feet² ⇒ rectangular face
* Lets add all of these areas to find the surface area of the solid
∴ The S.A = 60 + 342 + 60 + 36 + 24 + 36 + 24 = 582 feet²