What is the surface area of a rectangular pyramid with one side 12 mm, one side 15 mm, the base is 8 mm and one side 10 mm

Answer 1

To find the surface area of a rectangular pyramid, you need to calculate the area of the base and the area of each of the four triangular faces.

Given:
- Base length (l) = 8 mm
- Side length 1 (a) = 12 mm
- Side length 2 (b) = 15 mm
- Side length 3 (c) = 10 mm

Area of the base = l * w = 8 * 8 = 64 mm²

Now let's calculate the area of each of the four triangular faces.

For the first face:
- Base = l = 8 mm
- Height = √(12² - 8²) = √(144 - 64) = √80 = 8.94 mm
Area = 0.5 * base * height = 0.5 * 8 * 8.94 = 35.76 mm²

For the second face:
- Base = w = 15 mm
- Height = √(12² - 15²/4) = √(144 - 56.25) = √87.75 = 9.37 mm
Area = 0.5 * base * height = 0.5 * 15 * 9.37 = 70.31 mm²

For the third face:
- Base = a = 12 mm
- Height = √(15² - 12²/4) = √(225 - 36) = √189 = 13.75 mm
Area = 0.5 * base * height = 0.5 * 12 * 13.75 = 82.5 mm²

For the fourth face:
- Base = c = 10 mm
- Height = √(15² - 10²) = √(225 - 1) = √224 = 14.97 mm
Area = 0.5 * base * height = 0.5 * 10 * 14.97 = 74.85 mm²

Now, add up the areas of the base and the four triangular faces to get the total surface area.
Total surface area = 64 + 35.76 + 70.31 + 82.5 + 74.85 = 327.42 mm²

Therefore, the surface area of the rectangular pyramid is 327.42 mm².