find the surface area of a rectangular pyramid with these measurements 1=8yd w=4yd and h=2yd
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = Base Area + (0.5 × Perimeter of Base × Slant Height)
First, let's calculate the base area. The base of the pyramid is a rectangle, so its area can be calculated by multiplying the length and width:
Base Area = 8yd × 4yd = 32yd²
Next, let's calculate the slant height. The slant height can be found using the Pythagorean theorem:
Slant Height = √(w² + h²) = √(4yd² + 2yd²) = √(16yd² + 4yd²) = √20yd² = 2√5yd
Now, let's calculate the perimeter of the base. The perimeter of a rectangle can be calculated by adding the lengths of all four sides:
Perimeter of Base = 2 × (w + h) = 2 × (4yd + 2yd) = 2 × 6yd = 12yd
Finally, we can calculate the surface area:
Surface Area = 32yd² + (0.5 × 12yd × 2√5yd)
Surface Area = 32yd² + (6yd × 2√5yd)
Surface Area = 32yd² + 12yd√5yd
Surface Area = 32yd² + 12yd²√5
Surface Area = 44yd² + 12yd²√5
Therefore, the surface area of the rectangular pyramid is 44yd² + 12yd²√5.