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.
The area of the base is equal to the length multiplied by the width:
Area of base = l * w = 13cm * 11cm = 143cm^2
The area of each triangular face can be found by multiplying half the base length by the height of the pyramid:
Area of triangular face = 1/2 * l * h
There are four triangular faces, so the total surface area is:
Surface area = Area of base + 4 * Area of triangular face
Area of triangular face = 1/2 * l * h = 1/2 * 13cm * 8cm = 52cm^2
Surface area = 143cm^2 + 4 * 52cm^2 = 143cm^2 + 208cm^2 = 351cm^2
Therefore, the surface area of the rectangular pyramid is 351cm^2.
Find the surface area of a rectangular pyramid with these measurements: l = 13cm; w = 11 cm, and h = 8cm Express your answer as a decimal rounded to the nearest hundredth. (1 point)
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I apologize for the incorrect response. Let's try to find the surface area again.
The surface area of a rectangular pyramid can be calculated by finding the area of the base and the areas of the four triangular faces and then adding them together.
The area of the base is equal to the length multiplied by the width:
Area of base = l * w = 13cm * 11cm = 143cm^2
To find the area of each triangular face, we need to calculate the length of the slant height (which is the hypotenuse of the triangle) using the Pythagorean theorem. The slant height can be found using the height (h), the length (l), and the width (w) of the pyramid.
The slant height (s) can be calculated as follows:
s = sqrt(h^2 + (l/2)^2) = sqrt(8cm^2 + (13cm/2)^2) = sqrt(64cm^2 + 84.5cm^2) = sqrt(148.5cm^2) ≈ 12.18cm
Now we can calculate the area of each triangular face using the formula 1/2 * base * height:
Area of triangular face = 1/2 * l * s = 1/2 * 13cm * 12.18cm ≈ 78.99cm^2
Since there are four triangular faces, the total surface area is:
Surface area = Area of base + 4 * Area of triangular face
Surface area = 143cm^2 + 4 * 78.99cm^2 = 143cm^2 + 315.96cm^2 = 458.96cm^2
Therefore, the surface area of the rectangular pyramid is approximately 458.96cm^2, rounded to the nearest hundredth.
The surface area of a rectangular pyramid can be calculated by finding the area of the base and the areas of the four triangular faces and then adding them together.
The area of the base is equal to the length multiplied by the width:
Area of base = l * w = 13cm * 11cm = 143cm^2
To find the area of each triangular face, we need to calculate the length of the slant height (which is the hypotenuse of the triangle) using the Pythagorean theorem. The slant height can be found using the height (h), the length (l), and the width (w) of the pyramid.
The slant height (s) can be calculated as follows:
s = sqrt(h^2 + (l/2)^2) = sqrt(8cm^2 + (13cm/2)^2) = sqrt(64cm^2 + 84.5cm^2) = sqrt(148.5cm^2) ≈ 12.18cm
Now we can calculate the area of each triangular face using the formula 1/2 * base * height:
Area of triangular face = 1/2 * l * s = 1/2 * 13cm * 12.18cm ≈ 78.99cm^2
Since there are four triangular faces, the total surface area is:
Surface area = Area of base + 4 * Area of triangular face
Surface area = 143cm^2 + 4 * 78.99cm^2 = 143cm^2 + 315.96cm^2 = 458.96cm^2
Therefore, the surface area of the rectangular pyramid is approximately 458.96cm^2, rounded to the nearest hundredth.