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

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet