find the surface area of a rectangular pyramid with these measurements I=14m, w=10m, and h=15 round your answer to nearest hundredth keep in mind you have the height not the slant height
To find the surface area of a rectangular pyramid, we need to calculate the area of each face and add them up.
First, let's calculate the area of the base:
The area of a rectangle is given by the formula: A = length * width.
In this case, the length is 14m and the width is 10m, so the area of the base is A_base = 14m * 10m = 140m².
Next, let's calculate the area of each triangular face:
To find the area of a triangle, we need the base and height. Since we have the length (l) and height (h) of the pyramid, we can use Pythagoras' theorem to find the width of the triangular face.
The width (w) is the hypotenuse of a right triangle with legs of length h and l/2. Using Pythagoras' theorem, we can find w:
w = √(h² + (l/2)²)
w = √(15m² + (14m/2)²)
w = √(225m² + 49m²)
w = √(274m²)
w ≈ 16.55m
Now that we know the width of the triangular face, we can calculate its area:
A_triangle = (base * height) / 2
A_triangle = (10m * 16.55m) / 2
A_triangle ≈ 82.75m²
Since there are four triangular faces in a rectangular pyramid, the total area of the triangular faces is:
A_trianglar_faces = 4 * A_triangle
A_trianglar_faces = 4 * 82.75m²
A_trianglar_faces = 331m²
Finally, we can find the surface area by adding the area of the base and the area of the triangular faces:
Surface area = A_base + A_trianglar_faces
Surface area = 140m² + 331m²
Surface area = 471m²
Therefore, the surface area of the rectangular pyramid is 471m² (rounded to the nearest hundredth).