What is the surface area of the rectangular pyramid is 12mm, 10mm, 8mm, 15mm
The surface area of a rectangular pyramid can be calculated using the formula:
Surface area = Base area + (1/2) * Perimeter of base * Slant height
First, we need to find the base area of the pyramid. Since the base is a rectangle, the base area is given by length * width:
Base area = 12mm * 10mm = 120 mm^2
Next, we need to find the slant height of the pyramid. This can be found by using the Pythagorean theorem:
Slant height = sqrt((1/2 * base length)^2 + height^2)
Slant height = sqrt((1/2 * 12mm)^2 + 8mm^2)
Slant height = sqrt(6^2 + 8^2)
Slant height = sqrt(36 + 64)
Slant height = sqrt(100)
Slant height = 10 mm
Now, we can calculate the perimeter of the base:
Perimeter of base = 2 * (length + width)
Perimeter of base = 2 * (12mm + 10mm)
Perimeter of base = 2 * 22mm
Perimeter of base = 44 mm
Now, we can plug all these values into the formula for surface area:
Surface area = 120 mm^2 + (1/2) * 44mm * 10mm
Surface area = 120 mm^2 + 220 mm^2
Surface area = 340 mm^2
Therefore, the surface area of the rectangular pyramid is 340 mm^2.