what is the surface area of the rectangular pyramid? The base is 10 mm. the length is 8. The two slant heights are 12 and 15 mm.

Answer 1

To calculate the surface area of a rectangular pyramid, you need to find the surface area of the base and the lateral surface area.

The base of the rectangular pyramid is a rectangle with length 10 mm and width 8 mm, so the area of the base is
10 mm x 8 mm = 80 square mm.

The lateral surface area is the sum of the areas of the four triangular faces. To find the area of each triangle, you can use the formula for the area of a triangle: 0.5 x base x height.

For the triangle with a slant height of 12 mm:
Base = 10 mm
Height = 12 mm
Area = 0.5 x 10 mm x 12 mm = 60 square mm

For the triangle with a slant height of 15 mm:
Base = 8 mm
Height = 15 mm
Area = 0.5 x 8 mm x 15 mm = 60 square mm

Now, calculate the total lateral surface area:
2 triangles with slant height 12 mm = 2 x 60 square mm = 120 square mm
2 triangles with slant height 15 mm = 2 x 60 square mm = 120 square mm
Total lateral surface area = 120 square mm + 120 square mm = 240 square mm

Add the area of the base and the lateral surface area to find the total surface area of the rectangular pyramid:
Total surface area = base area + lateral surface area
Total surface area = 80 square mm + 240 square mm = 320 square mm

Therefore, the surface area of the rectangular pyramid is 320 square mm.