Find the surface area of a rectangular pyramid with these measurements length equals 8 cm with equals 4 cm and height equals 2 cm express your answer as a decimal rounded to the nearest hundredth
The surface area of a rectangular pyramid is given by the formula:
Surface Area = lateral area + base area
The lateral area can be found by multiplying the perimeter of the base by half the slant height. The slant height can be found using the Pythagorean theorem.
First, let's find the slant height:
h = height = 2 cm
a = length of base = 8 cm
b = width of base = 4 cm
Using the Pythagorean theorem: c^2 = a^2 + b^2
c^2 = 8^2 + 4^2
c^2 = 64 + 16
c^2 = 80
c = √80
c ≈ 8.94 cm
The perimeter of the base is given by: P = 2a + 2b
P = 2(8) + 2(4)
P = 16 + 8
P = 24 cm
The lateral area is given by: Lateral Area = (1/2) P * s
Lateral Area = (1/2)(24 cm)(8.94 cm)
Lateral Area ≈ 107.52 cm²
The base area is given by: Base Area = a * b
Base Area = (8 cm)(4 cm)
Base Area = 32 cm²
Finally, we can calculate the surface area:
Surface Area = Lateral Area + Base Area
Surface Area ≈ 107.52 cm² + 32 cm²
Surface Area ≈ 139.52 cm²
Therefore, the surface area of the rectangular pyramid is approximately 139.52 cm².