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.
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The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = base area + lateral area
The base area can be found by multiplying the length (l) by the width (w):
Base area = l * w = 8 cm * 4 cm = 32 cm^2
The lateral area can be found by calculating the area of each of the four triangular faces and summing them up.
To find the area of a triangular face, we need the base and height of the triangles. The base of each triangle is the width (w) of the pyramid, and the height of each triangle is the height (h) of the pyramid.
Area of one triangular face = (w * h) / 2 = (4 cm * 2 cm) / 2 = 8 cm^2
Since there are four triangular faces, the total lateral area is:
Lateral area = 4 * (w * h) / 2 = 4 * (4 cm * 2 cm) / 2 = 16 cm^2
Now, we can calculate the total surface area by summing the base area and lateral area:
Surface Area = base area + lateral area = 32 cm^2 + 16 cm^2 = 48 cm^2
Therefore, the surface area of the rectangular pyramid is 48 cm^2.
To find the surface area of a rectangular pyramid, you need to calculate the areas of all its faces and then add them up.
A rectangular pyramid has 5 faces: the base and four triangular faces.
First, let's calculate the area of the base. The base of the pyramid is a rectangle, so its area is given by:
Area of the base = length (l) * width (w)
Plugging in the given values, we have:
Area of the base = 8 cm * 4 cm = 32 square cm
Next, let's calculate the area of each triangular face. The formula for the area of a triangle can be given as:
Area of a triangle = (1/2) * base * height
For the triangular faces, the base is equal to the length (l) and the height is equal to the height (h) of the pyramid. Plugging in the given values, we have:
Area of each triangular face = (1/2) * 8 cm * 2 cm = 8 square cm
Since there are four triangular faces, the total area of the triangular faces is 4 * 8 square cm = 32 square cm.
Finally, to find the surface area of the rectangular pyramid, we add the area of the base and the total area of the triangular faces:
Surface area = Area of the base + Total area of triangular faces
= 32 square cm + 32 square cm
= 64 square cm
So, the surface area of the rectangular pyramid is 64 square cm.
Apologies for the mistake. Let's recalculate the surface area of the rectangular pyramid with the correct measurements.
The base area is given by the formula: base area = l * w, so base area = 8 cm * 4 cm = 32 cm².
Next, we need to calculate the area of each triangular face to find the lateral area. The area of a triangle can be found using the formula: area = 0.5 * base * height.
For the pyramid, the base of each triangle is the width (w), and the height of each triangle is the height (h). So, the area of each triangular face is: area = 0.5 * 4 cm * 2 cm = 4 cm².
Since there are 4 triangular faces, the total lateral area is: lateral area = 4 * 4 cm² = 16 cm².
Finally, we can calculate the surface area by summing the base area and the lateral area: surface area = base area + lateral area = 32 cm² + 16 cm² = 48 cm².
Therefore, the surface area of the rectangular pyramid is 48 cm².