Question

Please help me with #3.

Answer 1

Total lateral surface of the pyramid = 54
`cm^(2)`

which agrees with the first listed answer.

Explanation:

Notice that the pyramid has for base an equilateral triangle of base 5 cm, and has three lateral triangles which have all the same dimensions for their base (5 cm - since they are all connected to the base of the pyramid), and their height (7.2 cm).

The actual LATERAL surface, includes only the surface of the three lateral triangles.

We use the formula for the area of a triangle:
`Area=(base \,*\, height)/(2)`

to calculate the area of each lateral triangle:

`Area=(5\,cm \,*\, 7.2\,cm)/(2) \\Area=18 \,cm^2`

and then multiply the result by three (to account for the three lateral faces)

Therefore, the total lateral surface is:

Total lateral surface = 3 * 18 = 54
`cm^(2)`