Question

if W = 12 units, X = 5 units, Y = 9 units, and Z = 11 units, what is the surface area of the right rectangular pyramid shown ?

Answer 1

To find the surface area of a right rectangular pyramid, we need to add the area of the base to the area of the three lateral faces.

The base of the pyramid is a rectangle with dimensions length = X = 5 units and width = Y = 9 units.

Area of the base = length × width
= 5 units × 9 units
= 45 square units

To find the area of the lateral faces, we need to find the slant height of the pyramid.

The slant height can be found using the Pythagorean theorem:
Slant height, s = √(W^2 + (0.5Y)^2)
= √(12^2 + (0.5*9)^2)
= √(144 + 20.25)
= √164.25
= 12.81 units

Now, the area of each lateral face is a triangle with base equal to the width of the base (Y = 9 units) and height equal to the slant height (s = 12.81 units).

Area of each lateral face = 0.5 × base × height
= 0.5 × 9 units × 12.81 units
= 57.645 square units

There are three identical lateral faces, so the total area of the lateral faces = 3 × 57.645 square units = 172.935 square units

Therefore, the total surface area of the right rectangular pyramid = area of the base + area of the lateral faces
= 45 square units + 172.935 square units
= 217.935 square units

Therefore, the surface area of the right rectangular pyramid shown is 217.935 square units.