what is the surface area of the rectangular pyramid? the length is 12 cm and the angled height from the center of the length is 10.6 cm the base is 14 cm and the angled height from the center of the base is 10 cm
To find the surface area of a rectangular pyramid, we need to calculate the area of each of its sides and the base, and then add them all together.
First, we calculate the area of the base:
Area of the base = length x width
Area of the base = 12 cm x 14 cm
Area of the base = 168 cm²
Next, we calculate the area of each of the triangular faces.
To find the area of the triangle formed by the center of the length and the slant height:
Area = 0.5 x base x height
Area = 0.5 x 12 cm x 10.6 cm
Area = 63.6 cm²
To find the area of the triangle formed by the center of the base and the slant height:
Area = 0.5 x base x height
Area = 0.5 x 14 cm x 10 cm
Area = 70 cm²
Now, we calculate the total surface area:
Total surface area = 2 x base area + 2 x triangle area
Total surface area = 2(168 cm²) + 2(63.6 cm² + 70 cm²)
Total surface area = 2(168 cm²) + 2(133.6 cm²)
Total surface area = 336 cm² + 267.2 cm²
Total surface area = 603.2 cm²
Therefore, the surface area of the rectangular pyramid is 603.2 cm².