To find the surface area of a rectangular pyramid, we need to calculate the area of the base and the area of the four triangles surrounding the base.
1. Area of the base:
Base area = length x width
Base area = 14 cm x 12 cm
Base area = 168 cm²
2. Area of each triangular face:
First, we need to find the height of the pyramid using Pythagorean theorem:
h = sqrt((slant height)^2 - (base/2)^2)
h = sqrt(10.6^2 - 7^2)
h = sqrt(112.36 - 49)
h = sqrt(63.36)
h ≈ 7.96 cm
Area of each triangular face = 1/2 x base x height
Area of each triangular face = 1/2 x 12 cm x 7.96 cm
Area of each triangular face ≈ 47.76 cm²
3. Total surface area:
Total surface area = Base area + 4 x Area of each triangular face
Total surface area = 168 cm² + 4 x 47.76 cm²
Total surface area = 168 cm² + 191.04 cm²
Total surface area ≈ 359.04 cm²
Therefore, the surface area of the rectangular pyramid is approximately 359.04 cm².
What is the surface area of the rectangular pyramid? (1 point)
? cm^2
Slant Hight: 10.6cm and 10cm
Base: 14cm
side:12cm
3 answers
step by step
Sure! Here is a step-by-step breakdown of how to calculate the surface area of the rectangular pyramid:
Given:
Slant Height (l): 10.6 cm
Base (b): 14 cm
Side (s): 12 cm
Step 1: Calculate the height of the pyramid using Pythagorean theorem.
h = √(l^2 - (b/2)^2)
h = √(10.6^2 - (14/2)^2)
h = √(112.36 - 49)
h = √63.36
h ≈ 7.96 cm
Step 2: Calculate the base area.
Base area (A_base) = length x width
A_base = b x s
A_base = 14 cm x 12 cm
A_base = 168 cm²
Step 3: Calculate the area of each triangular face.
Area of each triangular face = 0.5 x base x height
Area of each triangular face = 0.5 x b x h
Area of each triangular face = 0.5 x 14 cm x 7.96 cm
Area of each triangular face ≈ 47.76 cm²
Step 4: Calculate the total surface area.
Total surface area (A_total) = A_base + 4 x Area of each triangular face
A_total = 168 cm² + 4 x 47.76 cm²
A_total = 168 cm² + 191.04 cm²
A_total ≈ 359.04 cm²
Therefore, the surface area of the rectangular pyramid is approximately 359.04 cm².
Given:
Slant Height (l): 10.6 cm
Base (b): 14 cm
Side (s): 12 cm
Step 1: Calculate the height of the pyramid using Pythagorean theorem.
h = √(l^2 - (b/2)^2)
h = √(10.6^2 - (14/2)^2)
h = √(112.36 - 49)
h = √63.36
h ≈ 7.96 cm
Step 2: Calculate the base area.
Base area (A_base) = length x width
A_base = b x s
A_base = 14 cm x 12 cm
A_base = 168 cm²
Step 3: Calculate the area of each triangular face.
Area of each triangular face = 0.5 x base x height
Area of each triangular face = 0.5 x b x h
Area of each triangular face = 0.5 x 14 cm x 7.96 cm
Area of each triangular face ≈ 47.76 cm²
Step 4: Calculate the total surface area.
Total surface area (A_total) = A_base + 4 x Area of each triangular face
A_total = 168 cm² + 4 x 47.76 cm²
A_total = 168 cm² + 191.04 cm²
A_total ≈ 359.04 cm²
Therefore, the surface area of the rectangular pyramid is approximately 359.04 cm².
1 answer