To find 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.
1. Area of the base:
Area = length x width
Area = 8 mm x 10 mm
Area = 80 mm²
2. Area of each triangular face:
To find the area of a triangle, we use the formula: (1/2) x base x height
a. Triangular face with base 8 mm and height 12 mm:
Area = (1/2) x 8 mm x 12 mm
Area = 48 mm²
b. Triangular face with base 10 mm and height 12 mm:
Area = (1/2) x 10 mm x 12 mm
Area = 60 mm²
c. Triangular face with base 8 mm and height 15 mm:
Area = (1/2) x 8 mm x 15 mm
Area = 60 mm²
d. Triangular face with base 10 mm and height 15 mm:
Area = (1/2) x 10 mm x 15 mm
Area = 75 mm²
3. Total surface area:
Total surface area = area of the base + sum of the areas of the four triangular faces
Total surface area = 80 mm² + 48 mm² + 60 mm² + 60 mm² + 75 mm²
Total surface area = 323 mm²
Therefore, the surface area of the rectangular pyramid is 323 mm².