To find the surface area of a rectangular pyramid, you need to find the area of each face and add them all together.
1. Base face:
The base of the pyramid is a rectangle with dimensions l = 15 m and w = 12 m. The area of a rectangle is found by multiplying the length by the width. Therefore, the area of the base face is 15 m * 12 m = 180 m².
2. Lateral faces:
The rectangular pyramid has 4 lateral faces, which are triangles. To find the area of a triangle, you need the base and the height. The base of each triangular face is the same as the side length of the pyramid's base rectangle, which is l = 15 m.
The height of each triangular face can be found using the Pythagorean theorem. The height of the triangle is the slant height of the pyramid, and it can be found using the side lengths l = 15 m, w = 12 m, and h = 10 m. The formula is h_triangular = sqrt(l^2 + (w/2)^2).
Substituting the given values, we get:
h_triangular = sqrt(15^2 + (12/2)^2) = sqrt(225 + 36) = sqrt(261) ≈ 16.16 m (rounded to two decimal places).
Now, the area of each triangular face can be found using the formula for the area of a triangle, which is 0.5 * base * height.
Area_triangular = 0.5 * l * h_triangular = 0.5 * 15 m * 16.16 m ≈ 121.20 m² (rounded to two decimal places).
Since there are 4 triangular faces, the total area of the lateral faces is 4 * Area_triangular = 4 * 121.20 m² = 484.80 m².
3. Total surface area:
The total surface area of the pyramid is the sum of the base area and the lateral face area. Therefore, the surface area is:
180 m² (base) + 484.80 m² (lateral faces) = 664.80 m².
Therefore, the surface area of the rectangular pyramid is approximately 664.80 square meters.
Surface area of a rectangular pyramid with the measurements
l=15 m
w=12 m
h=10 m
1 answer
1 answer