Given:
• AB = 6 cm
,• SM = √15 cm
Let's solve for the following:
• 1) the base elevation AM.
Given that we have a regular triangular pyramid, the length of the three bases are equal.
AB = BC = AC
BM = BC/2 = 6/2 = 3 cm
To solve for AM, which is the height of the base, apply Pythagorean Theorem:
The base elevation of the pyramid is 5.2 cm.
• (2)., The elevation SO.
To find the elevation of the pyramid, apply Pythagorean Theorem:
Where:
SM = √15 cm
MO = AM/2 = 5.2/2 = 2.6 cm
Thus, we have:
Length of SO = 2.9 cm
• (3). Area of the base:
To find the area of the triangular base, apply the formula:
Thus, we have:
The area of the base is 15.6 square cm.
• (4). Area of the side surface.
Apply the formula:
Where:
p is the perimeter
h is the slant height, SM = √15 cm
Thus, we have:
• (5). Total surface area:
To find the total surface area, apply the formula:
Where:
Area of base = 15.6 cm²
Area of side surface = 34.86 cm²
TSA = 15.6 + 34.86 = 50.46 cm²
The total surface area is 50.46 cm²
• (6). Volume:
To find the volume, apply the formula:
Where:
Area of base = 15.6 cm²
Height, SO = 2.9 cm
Thus, we have:
The volume is 15.08 cm³.
ANSWER:
• 1.) 5.2 cm
,• 2.) 2.9 cm
,• 3.) 15.6 cm²
,• 4.) 34.86 cm²
,• (5). 50.46 cm²
,• 6). 15.08 cm³.