Find the surface area of rectangular pyramids
1. Length= 1.15ft Width=0.82 ft Height of the slanted face =3.17ft
Surface Area=7.1879ft^2
Formula for Rectangular Pyramid Surface Area : B+1/2pl
B=area of base
p=perimeter of base
l=height of slanted face
To find the surface area of a rectangular pyramid, we can use the formula: Surface Area = Area of Base + 1/2 * Perimeter of Base * Height of Slanted Face.
Let's calculate each part of the formula step by step:
1. Calculate the Area of Base (B):
For a rectangular pyramid, the base is a rectangle. The formula for the area of a rectangle is length * width.
Given:
Length = 1.15 ft
Width = 0.82 ft
Area of Base (B) = Length * Width = 1.15 ft * 0.82 ft = 0.943 ft^2
2. Calculate the Perimeter of Base (p):
For a rectangle, the perimeter is equal to 2 * (length + width).
Given:
Length = 1.15 ft
Width = 0.82 ft
Perimeter of Base (p) = 2 * (Length + Width) = 2 * (1.15 ft + 0.82 ft) = 4.94 ft
3. Calculate the Height of Slanted Face (l):
Given:
Height of Slanted Face = 3.17 ft
Height of Slanted Face (l) = 3.17 ft
4. Substitute the calculated values into the formula:
Surface Area = B + 1/2 * p * l
Surface Area = 0.943 ft^2 + 1/2 * 4.94 ft * 3.17 ft
Surface Area = 0.943 ft^2 + (1/2 * 15.6386 ft^2) = 0.943 ft^2 + 7.8193 ft^2 = 8.7623 ft^2
Hence, the surface area of the rectangular pyramid is approximately 8.7623 ft^2.