To calculate the surface area of a rectangular pyramid, we first need to find the area of the base and the area of each of the four triangular faces.
The area of the base (rectangle) is given by:
Area = length x width
Area = 10 cm x 10.6 cm
Area = 106 cm²
Next, we need to find the area of each of the four triangular faces. We can split the rectangular pyramid into two triangles with base 10 cm and height 12 cm, and two triangles with base 10.6 cm and height 12 cm.
The area of each triangular face is given by:
Area = 0.5 x base x height
For the first two triangles:
Area = 0.5 x 10 cm x 12 cm
Area = 60 cm²
For the other two triangles:
Area = 0.5 x 10.6 cm x 12 cm
Area = 63.6 cm²
Now, we can sum up the areas of the base and the four triangular faces to find the total surface area of the rectangular pyramid:
Total Surface Area = Base Area + 4 x Triangular Face Area
Total Surface Area = 106 cm² + 2 x 60 cm² + 2 x 63.6 cm²
Total Surface Area = 106 cm² + 120 cm² + 127.2 cm²
Total Surface Area = 353.2 cm²
Therefore, the surface area of the rectangular pyramid is 353.2 square centimeters.
Use the image to answer the question what is the surface area of a rectangular pyramid showing 10 cm 10.6 cm 14 cm 12 cm
What is the surface area of the rectangular pyramid in square centimeters?
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