Find the surface area of a rectangular pyramid with these measurements l=8 yd. W=4 yards and h=2 yd
The surface area of a rectangular pyramid can be calculated by finding the area of the base and adding the areas of the four triangular faces.
The area of the base is given by the formula: A_base = l * w, where l is the length and w is the width.
A_base = 8 yd * 4 yards = 32 square yards.
To calculate the area of the triangular faces, we need to find the length of the slant height (s). Since this is a rectangular pyramid, we can use the Pythagorean theorem and find s using the length (l), width (w), and height (h).
s^2 = (l/2)^2 + h^2
s^2 = (8/2)^2 + 2^2
s^2 = 4^2 + 4
s^2 = 16 + 4
s^2 = 20
s ≈ √20 = 4.47 yards (approx.)
Now, we can calculate the area of each triangular face using the formula: A_triangle = (1/2) * base * height, where the base is the length (l) and the height is the slant height (s).
A_triangle = (1/2) * 8 yards * 4.47 yards
A_triangle ≈ 17.88 square yards
Since there are four triangular faces, the total area of all the triangular faces combined is: 4 * A_triangle = 4 * 17.88 square yards = 71.52 square yards.
Finally, we can find the surface area of the rectangular pyramid by adding the area of the base and the area of the four triangular faces:
Surface area = A_base + A_triangles
Surface area = 32 square yards + 71.52 square yards
Surface area = 103.52 square yards.
Therefore, the surface area of the rectangular pyramid is 103.52 square yards.