Find the surface area of a rectangular pyramid with these measurements: l = 8 cm, w = 4 cm, and h = 2 cm. Express your answer as a decimal rounded to the nearest hundredth.
Pls help, I can't find the answer!!!
To find the surface area of a rectangular pyramid, you need to calculate the area of each of its faces, including the base.
The formula for the surface area of a rectangular pyramid is given by:
Surface Area = Base Area + 2 × (Length × Slant Height) + 2 × (Width × Slant Height)
To calculate the base area, you simply multiply the length and width of the base:
Base Area = Length × Width
In this case, the length (l) is 8 cm, and the width (w) is 4 cm, so the base area is:
Base Area = 8 cm × 4 cm = 32 cm^2
The slant height (s) can be found using the Pythagorean theorem:
s = sqrt(l^2 + h^2)
In this case, the height (h) is 2 cm, so plugging in the values, we get:
s = sqrt(8^2 + 2^2) = sqrt(68) ≈ 8.246 cm (rounded to three decimal places)
Now we can calculate the surface area using the formula mentioned above:
Surface Area = 32 cm^2 + 2 × (8 cm × 8.246 cm) + 2 × (4 cm × 8.246 cm)
Surface Area ≈ 32 cm^2 + 2 × 65.968 cm^2 + 2 × 32.984 cm^2
Surface Area ≈ 32 cm^2 + 131.936 cm^2 + 65.968 cm^2
Surface Area ≈ 229.904 cm^2
Therefore, the surface area of the rectangular pyramid is approximately 229.904 cm^2.
That's not it.......
Apologies for the incorrect response earlier. To find the surface area of a rectangular pyramid, we need to calculate the area of each of its faces separately and then sum them up.
The base of the pyramid is a rectangle, so the area of the base is simply the product of its length and width:
Base Area = l × w = 8 cm × 4 cm = 32 cm²
Now, let's calculate the area of the four triangular faces.
To calculate the area of each triangular face, we need the length of the base of the triangle and its height.
The length of the base of each triangular face is the same as the length of the base of the pyramid, which is 8 cm.
The height of each triangular face is equal to the height of the pyramid, which is 2 cm.
Thus, the area of each triangular face is:
Triangle Area = 0.5 × Base × Height = 0.5 × 8 cm × 2 cm = 8 cm²
Since there are four triangular faces, the total area of the triangular faces is:
Total Triangular Faces Area = 4 × Triangle Area = 4 × 8 cm² = 32 cm²
Now, we can calculate the surface area by summing up the area of the base and the total area of the triangular faces:
Surface Area = Base Area + Total Triangular Faces Area = 32 cm² + 32 cm² = 64 cm²
Therefore, the surface area of the rectangular pyramid is 64 cm².
That's not it either........
Apologies once again for the incorrect response earlier. Let's calculate the surface area of a rectangular pyramid with the given measurements correctly.
The formula to find the surface area of a rectangular pyramid is:
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 with length l = 8 cm and width w = 4 cm.
Base Area = l × w = 8 cm × 4 cm = 32 cm²
Next, let's calculate the perimeter of the base. Since the base is a rectangle, the perimeter is given by:
Perimeter of Base = 2 × (Length + Width) = 2 × (8 cm + 4 cm) = 2 × 12 cm = 24 cm
Now, let's calculate the slant height (s) using the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height (h) and the half of the base width (0.5w).
Using the given height h = 2 cm and base width w = 4 cm:
s = sqrt(h^2 + (0.5w)^2) = sqrt(2^2 + (0.5 × 4)^2) = sqrt(4 + 2^2) = sqrt(4 + 4) = sqrt(8) ≈ 2.83 cm (rounded to two decimal places)
Now, we can substitute the values into the Surface Area formula:
Surface Area = Base Area + (0.5 × Perimeter of Base × Slant Height)
Surface Area = 32 cm² + (0.5 × 24 cm × 2.83 cm)
Surface Area = 32 cm² + (12 cm × 2.83 cm)
Surface Area = 32 cm² + 33.96 cm²
Surface Area ≈ 65.96 cm²
Therefore, the surface area of the rectangular pyramid is approximately 65.96 cm².