Find the surface area of a rectangle 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
The surface area of a rectangular pyramid can be found using the formula:
Surface Area = l*w + l * sqrt((w/2)^2 + h^2) + w * sqrt((l/2)^2 + h^2)
Given:
l = 8 cm
w = 4 cm
h = 2 cm
Plugging in these values into the formula, we have:
Surface Area = 8*4 + 8 * sqrt((4/2)^2 + 2^2) + 4 * sqrt((8/2)^2 + 2^2)
Simplifying,
Surface Area = 32 + 8 * sqrt((2)^2 + 4) + 4 * sqrt((4)^2 + 4)
Surface Area = 32 + 8 * sqrt(4 + 4) + 4 * sqrt(16 + 4)
Surface Area = 32 + 8 * sqrt(8) + 4 * sqrt(20)
Surface Area ≈ 32 + 8 * 2.83 + 4 * 4.47
Surface Area ≈ 32 + 22.64 + 17.88
Surface Area ≈ 72.52
Therefore, the surface area of the rectangular pyramid is approximately 72.52 square centimeters.
To find the surface area of a rectangular pyramid, we need to calculate the area of each face and then sum them up.
The rectangular pyramid has a length of 8 cm, a width of 4 cm, and a height of 2 cm.
1. Base Area: The base of the pyramid is a rectangle with dimensions 8 cm by 4 cm. To find the area of the base, multiply the length by the width:
Base Area = 8 cm * 4 cm = 32 cm^2
2. Side Faces: The rectangular pyramid has 4 identical triangular side faces. To find the area of one side face, we need to calculate the area of the triangle formed by the height of the pyramid and one of the sides.
The height of the pyramid is 2 cm. Half the width is 4 cm/2 = 2 cm.
To find the area of the triangular face, we can use the formula: (1/2) * base * height. The base of the triangle is 4 cm, and the height is 2 cm.
Side Face Area (Triangle) = (1/2) * 4 cm * 2 cm = 4 cm^2
Since there are 4 identical side faces, the total area of the side faces is: 4 cm^2 * 4 = 16 cm^2
3. Total Surface Area: Finally, we sum up the base area and the total area of the side faces to find the total surface area of the triangular prism.
Total Surface Area = Base Area + Side Face Area
= 32 cm^2 + 16 cm^2
= 48 cm^2
Therefore, the surface area of the rectangular pyramid is 48 square centimeters.