To find the surface area of a rectangular pyramid, you need to find the area of the base and the area of each of the four triangular faces.
The base of the pyramid is a rectangle with sides of length 8 and 10, so the area of the base is:
Area of base = length × width = 8 × 10 = 80 square units.
Next, we need to find the areas of the four triangular faces. These triangles are right triangles and have legs that are the slant heights of the pyramid. The slant heights are given as 12 and 15.
The areas of the triangular faces can be calculated using the formula for the area of a triangle:
Area = 1/2 × base × height.
For one of the triangular faces with slant height 12:
Area = 1/2 × 8 × 12 = 48 square units.
For the other triangular face with slant height 15:
Area = 1/2 × 10 × 15 = 75 square units.
Since there are four triangular faces on the rectangular pyramid, the total area of all the triangular faces is:
Total area of triangular faces = 4 × (48 + 75) = 492 square units.
Therefore, the total surface area of the rectangular pyramid is the sum of the base area and the area of the four triangular faces:
Surface area = 80 + 492 = 572 square units.
So, the surface area of the rectangular pyramid with bases 8 and 10 and slant heights 12 and 15 is 572 square units.
What is the surface area of the rectangular pyramid with bases 8 and 10 and slant heights 12 and 15
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