Answer:
The total surface area = 10956 m²
Explanation:
∵ The pyramid is rectangular pyramid
∴ It has a rectangular base with dimensions of 50 m and 78 m
∴ It has four faces each two opposite are congruent
* to find the total surface area, we will find the area of
each face and add them together
- Area base = L × W
∴ Area base = 50 × 78 = 3900 m² ⇒ (1)
- Area of triangular face of dimensions:
base = 50 m and height = 60 m
∵ Area triangle = 1/2 × base × height
∴ Area triangle = 1/2 × 50 × 60 = 1500 m²
∵ We have another triangle congruent to this triangle (opposite faces)
∴ Area of the two congruent faces = 1500 × 2 = 3000 m² ⇒ (2)
- Area of triangular face of dimensions:
base = 78 m and height = 52 m
∵ Area triangle = 1/2 × base × height
∴ Area triangle = 1/2 × 78 × 52 = 2028 m²
∵ We have another triangle congruent to this triangle (opposite faces)
∴ Area of the two congruent faces = 2028 × 2 = 4056 m² ⇒ (3)
∴ Add (1) , (2) and (3)
∴ The total surface area = 3900 + 3000 + 4056 = 10956 m²