To find the surface area of a rectangular pyramid, you need to first calculate the area of the base and the area of the four triangular faces.
The area of the base is given by:
Area of base = length x width
Area of base = 15mm x 12mm
Area of base = 180 mm²
Next, calculate the area of the four triangular faces. Each triangular face has a base equal to the length of the rectangular base (15mm) and a height equal to the slant height of the pyramid. The slant height can be calculated using the Pythagorean theorem:
slant height = sqrt(base^2 + height^2)
slant height = sqrt(8^2 + 10^2)
slant height = sqrt(64 + 100)
slant height = sqrt(164)
slant height ≈ 12.81 mm
Now, calculate the area of one triangular face and multiply it by 4 to account for all four faces:
Area of one triangular face = (1/2) x base x height
Area of one triangular face = (1/2) x 15mm x 12.81mm
Area of one triangular face ≈ 96.075 mm²
Total area of four triangular faces = 4 x 96.075 mm² = 384.3 mm²
Finally, calculate the total surface area of the rectangular pyramid by adding the base area and the four triangular faces:
Surface area = area of base + total area of four triangular faces
Surface area = 180 mm² + 384.3 mm²
Surface area ≈ 564.3 mm²
Therefore, the surface area of the rectangular pyramid is approximately 564.3 mm².
Use the image to answer the question what is the surface area of a rectangular pyramid
The image shows on the left side 12 MM on the top right side 15 MM the bottom 8mm right lower 10 mm
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