Question
What is the surface area for the rectangular pyramid? The sides are l=18 w=16 b face=11, right face= 12
Answers
Answered by
GPT 3.5
To calculate the surface area of a rectangular pyramid, you first need to find the area of each face.
1. The base of the pyramid is a rectangle with length l = 18 and width w = 16. The area of the base is:
Area of base = l x w
Area of base = 18 x 16
Area of base = 288 square units
2. The side faces of the pyramid are triangles. To find the area of a triangle, you need the base and height. The base of the triangles is the side length of the base rectangle, and the height is the slant height of the pyramid. To find the slant height, you can use the Pythagorean theorem:
Slant height = √(h^2 + (1/2*b)^2)
Slant height = √(11^2 + (1/2*16)^2)
Slant height = √(121 + 64)
Slant height = √185
Slant height ≈ 13.6
Now, the area of one of the triangular side faces is:
Area of side face = (1/2) x base x height
Area of side face = (1/2) x 11 x 13.6
Area of side face ≈ 74.8 square units
3. The other side face has a base of 16 and height of 12. The area is:
Area of side face = (1/2) x base x height
Area of side face = (1/2) x 16 x 12
Area of side face = 96 square units
Now, to find the total surface area of the rectangular pyramid, add up all the areas:
Total surface area = Area of base + 2 x Area of side faces
Total surface area = 288 + 74.8 + 96
Total surface area = 458.8 square units
Therefore, the surface area of the rectangular pyramid is 458.8 square units.
1. The base of the pyramid is a rectangle with length l = 18 and width w = 16. The area of the base is:
Area of base = l x w
Area of base = 18 x 16
Area of base = 288 square units
2. The side faces of the pyramid are triangles. To find the area of a triangle, you need the base and height. The base of the triangles is the side length of the base rectangle, and the height is the slant height of the pyramid. To find the slant height, you can use the Pythagorean theorem:
Slant height = √(h^2 + (1/2*b)^2)
Slant height = √(11^2 + (1/2*16)^2)
Slant height = √(121 + 64)
Slant height = √185
Slant height ≈ 13.6
Now, the area of one of the triangular side faces is:
Area of side face = (1/2) x base x height
Area of side face = (1/2) x 11 x 13.6
Area of side face ≈ 74.8 square units
3. The other side face has a base of 16 and height of 12. The area is:
Area of side face = (1/2) x base x height
Area of side face = (1/2) x 16 x 12
Area of side face = 96 square units
Now, to find the total surface area of the rectangular pyramid, add up all the areas:
Total surface area = Area of base + 2 x Area of side faces
Total surface area = 288 + 74.8 + 96
Total surface area = 458.8 square units
Therefore, the surface area of the rectangular pyramid is 458.8 square units.