Find the Surface Area of the Rectangular Pyramid.
Length = 6
Width = 6
Height = 13
Slant Heigh = 13.3
There are different methods to find the surface area of a pyramid, but one common way is to add the areas of the five faces. In a rectangular pyramid, there are four triangular faces that are congruent (meaning they have the same size and shape) and one rectangular face that is the base. To find the surface area, we need to find the area of each face.
The area of a triangle can be found using the formula:
Area = 1/2 * base * height
where the base and height are perpendicular (at right angles) to each other. In a triangular face of the pyramid, the base is one of the sides of the rectangle base, and the height is the slant height of the pyramid (the segment from the vertex of the triangle to the midpoint of the opposite edge).
Using the given measurements, we can find the area of each triangular face as:
Area = 1/2 * base * height
Area = 1/2 * 6 * 13.3
Area = 39.9 (rounded to one decimal place)
There are four triangular faces, so the total area of the triangular faces is:
4 * 39.9 = 159.6
The area of the rectangular base can be found using the formula:
Area = length * width
Using the given measurements, we can find the area of the base as:
Area = 6 * 6
Area = 36
The total surface area of the rectangular pyramid is the sum of the areas of the five faces:
Surface Area = area of base + area of four triangular faces
Surface Area = 36 + 159.6
Surface Area = 195.6
Therefore, the surface area of the rectangular pyramid is 195.6 square units.
To find the surface area of a rectangular pyramid, you need to calculate the areas of each of its faces and add them together.
1. Calculate the base area:
The base of the rectangular pyramid is a rectangle with length and width given.
Base area = Length * Width = 6 * 6 = 36 square units
2. Calculate the area of each triangular face:
Each triangular face has a base equal to the width of the rectangular pyramid and a height equal to the slant height.
Area of each triangular face = (1/2) * Base * Height
Area of each triangular face = (1/2) * 6 * 13.3 = 39.9 square units
3. Since there are four identical triangular faces, the total area of these faces is 4 times the area of one face.
Total area of triangular faces = 4 * Area of one triangular face
Total area of triangular faces = 4 * 39.9 = 159.6 square units
4. Finally, calculate the surface area by summing the base area and the total area of the triangular faces.
Surface area of the rectangular pyramid = Base area + Total area of triangular faces
Surface area = 36 + 159.6 = 195.6 square units
Therefore, the surface area of the rectangular pyramid is 195.6 square units.