Find the surface area of a rectangular pyramid with these measurements l = 15 m, w= 12m and h = 10 m. Express your answer as a decimal rounded to the nearest hundredth
To find the surface area of a rectangular pyramid, we need to find the area of the base and the area of each triangular face.
The area of the base is given by the formula: A = l * w, where l is the length and w is the width.
So, the area of the base is A = 15 m * 12 m = 180 m^2.
The area of each triangular face is given by the formula: A = (1/2) * base * height, where base is the length of the base of the triangle (equal to the length or width of the base of the pyramid), and height is the height of the pyramid.
The height of each triangular face is given by h = 10 m.
For the first triangular face, the base is the length of the base of the pyramid, l = 15 m. So, the area of the first triangular face is A1 = (1/2) * 15 m * 10 m = 75 m^2.
For the second triangular face, the base is the width of the base of the pyramid, w = 12 m. So, the area of the second triangular face is A2 = (1/2) * 12 m * 10 m = 60 m^2.
For the third triangular face, the base is the length of the base of the pyramid, l = 15 m. So, the area of the third triangular face is A3 = (1/2) * 15 m * 10 m = 75 m^2.
For the fourth triangular face, the base is the width of the base of the pyramid, w = 12 m. So, the area of the fourth triangular face is A4 = (1/2) * 12 m * 10 m = 60 m^2.
The surface area of the rectangular pyramid is the sum of the areas of the base and the four triangular faces:
Surface Area = A + A1 + A2 + A3 + A4 = 180 m^2 + 75 m^2 + 60 m^2 + 75 m^2 + 60 m^2 = 450 m^2.
Therefore, the surface area of the rectangular pyramid is 450 m^2.
To find the surface area of a rectangular pyramid, we need to calculate the area of the base and the area of the four triangular faces.
First, let's find the area of the base:
The base of a rectangular pyramid is a rectangle, so we can use the formula for the area of a rectangle: A = length × width.
The length is given as l = 15 m and the width is given as w = 12 m.
Therefore, the area of the base is A_base = l × w = 15 m × 12 m = 180 m².
Next, let's find the area of the four triangular faces:
Each triangular face has a base equal to the length of the rectangular base and a height equal to the height of the pyramid.
The base (b) is l = 15 m, and the height (h) is given as h = 10 m.
Therefore, the area of each triangular face is A_triangle = 0.5 × b × h = 0.5 × 15 m × 10 m = 75 m².
Since there are four triangular faces in a rectangular pyramid, the total area of the four triangular faces is 4 × A_triangle = 4 × 75 m² = 300 m².
Finally, to find the surface area of the rectangular pyramid, we sum the area of the base and the area of the four triangular faces:
Surface Area = A_base + Total Area of the Four Triangular Faces = 180 m² + 300 m² = 480 m².
Therefore, the surface area of the rectangular pyramid is 480 m².