what is the surface area of the rectangular pyramid 12 mm, 10 mm, 15 mm, 8 mm ?????/

Question

_____, mm2

Answer 1

First, we need to calculate the surface area of each face of the pyramid.

The base of the pyramid is a rectangle with dimensions 12 mm and 10 mm. The area of the base is:

Base area = length x width
Base area = 12 mm x 10 mm
Base area = 120 mm2

Now, let's calculate the area of the four triangular faces:

1. First triangular face:
Height = 15 mm
Base = 12 mm
Area = (1/2) x base x height
Area = (1/2) x 12 mm x 15 mm
Area = 90 mm2

2. Second triangular face:
Height = 15 mm
Base = 10 mm
Area = (1/2) x base x height
Area = (1/2) x 10 mm x 15 mm
Area = 75 mm2

3. Third triangular face:
Height = 8 mm
Base = 12 mm
Area = (1/2) x base x height
Area = (1/2) x 12 mm x 8 mm
Area = 48 mm2

4. Fourth triangular face:
Height = 8 mm
Base = 10 mm
Area = (1/2) x base x height
Area = (1/2) x 10 mm x 8 mm
Area = 40 mm2

Now, we sum up the areas of the base and the four triangular faces to get the total surface area of the pyramid:

Total surface area = Base area + 4 x Triangular face area
Total surface area = 120 mm2 + 90 mm2 + 75 mm2 + 48 mm2 + 40 mm2
Total surface area = 373 mm2

Therefore, the surface area of the rectangular pyramid is 373 mm2.