Find the surface area of a rectangular pyramid with these measurements: l = 13 cm, w = 11 cm, and h = 8 cm. Express your answer as a decimal rounded to the nearest hundredth. solve this by Using the formula for surface area in parts
To find the surface area of a rectangular pyramid, we use the formula:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
First, let's calculate the base area:
Base Area = l * w
Base Area = 13 cm * 11 cm
Base Area = 143 cm²
Next, let's calculate the perimeter of the base:
Perimeter of Base = 2 * (l + w)
Perimeter of Base = 2 * (13 cm + 11 cm)
Perimeter of Base = 2 * 24 cm
Perimeter of Base = 48 cm
Now, let's calculate the slant height. In a rectangular pyramid, the slant height can be calculated using the Pythagorean theorem. The slant height (s) is the hypotenuse of a right triangle with the height (h) as one side and the slant height (s) as the other side:
s² = h² + (1/2 * l)²
s² = 8 cm² + (1/2 * 13 cm)²
s² = 64 cm² + (6.5 cm)²
s² = 64 cm² + 42.25 cm²
s² = 106.25 cm²
s = √106.25 cm ≈ 10.31 cm
Finally, let's calculate the surface area:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
Surface Area = 143 cm² + (1/2) * 48 cm * 10.31 cm
Surface Area = 143 cm² + 24.155 cm²
Surface Area ≈ 167.16 cm²
Therefore, the surface area of the rectangular pyramid is approximately 167.16 cm².