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.
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The surface area of a rectangular pyramid can be found by adding the area of the base to the sum of the areas of the four triangular faces.
Area of the base = length * width = 13 cm * 11 cm = 143 cm²
Now let's calculate the area of each triangular face.
The first triangular face has a base equal to the length (13 cm) and a height equal to the height of the pyramid (8 cm).
Area of the first triangular face = (13 cm * 8 cm) / 2 = 52 cm²
Since there are four triangular faces, the total area of the triangular faces is 4 times the area of the first triangular face.
Total area of the triangular faces = 4 * 52 cm² = 208 cm²
Now we can calculate the surface area of the rectangular pyramid by adding the area of the base to the total area of the triangular faces.
Surface area of the rectangular pyramid = Area of the base + Total area of the triangular faces = 143 cm² + 208 cm² = 351 cm²
Therefore, the surface area of the rectangular pyramid with the given measurements is 351 cm².
The surface area of a rectangular pyramid can be calculated by finding the area of the base and the area of the four triangular faces and adding them together.
The area of the base can be found by multiplying the length (l) by the width (w).
Area of base = l * w = 13 cm * 11 cm = 143 cm²
The four triangular faces all have the same area, which can be calculated by finding the area of one of them and multiplying by 4.
The area of a triangular face can be found by multiplying the length (l) by the height (h) and dividing by 2.
Area of a triangular face = (l * h) / 2 = (13 cm * 8 cm) / 2 = 52 cm²
Total area of all four triangular faces = 52 cm² * 4 = 208 cm²
Now we can find the total surface area by adding the area of the base and the area of all four triangular faces together.
Total surface area = Area of base + Total area of all four triangular faces
= 143 cm² + 208 cm²
= 351 cm²
Therefore, the surface area of the rectangular pyramid is 351 cm².
To find the surface area of a rectangular pyramid, we need to determine the areas of its individual faces and then sum them up.
A rectangular pyramid has 5 faces: the base and four triangular faces. The base of the pyramid is a rectangle with dimensions of length (l) and width (w). Therefore, the area of the base can be calculated by multiplying the length and width: A_base = l * w.
Each triangular face has a base equal to the length (l) of the pyramid and a height (h) equal to the height of the pyramid. The area of a triangle can be calculated using the formula: A_triangle = 1/2 * base * height. Plugging in the values for the base and height, we get: A_triangle = 1/2 * l * h.
In this case, we have 4 triangular faces, so the total area of the triangular faces is: A_triangular_faces = 4 * A_triangle.
Finally, we can calculate the total surface area by summing up the area of the base and the triangular faces: A_total = A_base + A_triangular_faces.
Let's calculate the surface area of the rectangular pyramid with the given measurements:
A_base = 13 cm * 11 cm = 143 cm^2
A_triangle = 1/2 * 13 cm * 8 cm = 52 cm^2
A_triangular_faces = 4 * 52 cm^2 = 208 cm^2
A_total = 143 cm^2 + 208 cm^2 = 351 cm^2
Therefore, the surface area of the rectangular pyramid is 351 cm^2 rounded to the nearest hundredth.