Answer:
V = 205 Km³
Step-by-step explanation:
The volume (V) of a pyramid is calculated as
• V = [tex]\frac{1}{3}[/tex] Ah ( A is the area of the base and h the height )
The area (A) of a regular polygon is
• A = [tex]\frac{1}{2}[/tex] pa ( p is the perimeter and a the apothem )
An apothem is a segment that joins the polygon's centre to the midpoint of any side and is perpendicular to that side.
here perimeter p = 5 × 6 Km = 30 Km and apothem = 4.1 Km
Then
A = [tex]\frac{1}{2}[/tex] × 30 × 4.1 = 15 × 4.1 = 61.5 Km² and h = 10 Km
Then
V = [tex]\frac{1}{3}[/tex] × 61.5 × 10 = [tex]\frac{1}{3}[/tex] × 615 = 205 Km³
