MATH SOLVE

3 months ago

Q:
# What is the total surface area of this rectangular pyramid? square meters

Accepted Solution

A:

Answer:The total surface area = 10956 m²Step-by-step 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