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 twice the area of the top
twice the area of an end twice the area of a side
To find the surface area of a rectangular pyramid, we can use the formula:
Surface Area = Area of the Base + Area of the 4 Triangular Faces
The base of the pyramid is a rectangle with length (l) and width (w), so the area of the base can be found by multiplying the length and width:
Area of the Base = l * w
In this case, l = 13 cm and w = 11 cm, so:
Area of the Base = 13 cm * 11 cm = 143 cm^2
The pyramid also has 4 triangular faces. Each triangular face has a base equal to the rectangle's width (11 cm) and a height equal to the height of the pyramid (h = 8 cm). Therefore, the area of each triangular face can be found by multiplying the base and height and dividing by 2:
Area of a Triangular Face = (w * h) / 2
In this case, w = 11 cm and h = 8 cm, so:
Area of a Triangular Face = (11 cm * 8 cm) / 2 = 44 cm^2
Since there are 4 triangular faces, the total area of all four is:
Total Area of 4 Triangular Faces = 4 * Area of a Triangular Face = 4 * 44 cm^2 = 176 cm^2
Finally, we can calculate the total surface area by adding the area of the base and the total area of the triangular faces:
Surface Area = Area of the Base + Total Area of 4 Triangular Faces
Surface Area = 143 cm^2 + 176 cm^2
Surface Area = 319 cm^2
Therefore, the surface area of the rectangular pyramid is 319 cm^2 rounded to the nearest hundredth.