If X = 4 units, Y = 3 units, and Z = 6 units, then what is the surface area of the right triangular pyramid shown above?

A. 48 square units

B. 36 square units

C. 42 square units

D. 22.5 square units

C. 42

Step-by-step explanation:

Since the triangle making up the base of the right triangular pyramid is equilateral, the three lateral triangles will have equal areas. To find the surface area of the pyramid, find the area of one of the lateral triangles and multiply it by 3. Then, add that to the area of the triangle that forms the base.

Area of Lateral Triangle = 1/2 · base · height

                                       = 1/2 · X · Z

                                      = 1/2 ·  4 units ·  6 units

                                      = 12 square units

Area of Base Triangle = 1/2 ·  base ·  height

                                    = 1/2 ·  X ·  Y

                                    = 1/2 ·  4 units ·  3 units

                                   = 6 square units

Now, use the method described above to find the surface area of the pyramid.

Surface Area = 3( Area lateral ) + ( Area base )

                     = 3 ( 12 square units ) + ( 6 square units )

                    = 42 square units

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.