In the diagram of the base of the hexagonal pyramid, all the triangles are the same. Find the surface area of the hexagonal pyramid.
Answers
Answer:
Question:
What would the surface area of a hexagonal pyramid be if one of the base sides is 5 cm and the slant height is 6.9 cm?
The surface area (SA) is the lateral area (LA) plus the area of the base (B).
SA=LA+B
Because a slant height is given the pyramid must be a regular pyramid. Therefor, each of the later faces are congruent isosceles triangles. The easiest way to find the lateral area is to use the formula LA=12p l
Where: p is the perimeter of the base and l is the slant height.
LA=12(30)(6.9)cm2=103.5cm2
If you do not like formulas, find the area of one of the lateral faces and then multiple by the number of lateral faces.
Since the pyramid is regular, the base must be a regular polygon. The area of a regular polygon is B=12ap
Where: a is the apothem and p is the perimeter.
B=12(2.53–√)(30)cm2=37.53–√cm2
SA=LA+B=(103.5+37.53–√)cm2≈168.4519053cm2
Step-by-step explanation: