Answer:
The pentagonal pyramid has a base area of 61.94m² or 61.94 square metres.
Explanation:
The formula for a Right Pentagonal pyramid is given as:
Volume = 5/12× tan(54°) × height × (Base edge)²
In the question above, we are asked to find the base area of the Pentagonal pyramid.
Step 1
The first step would be to first find the Bases edge of the Pentagonal pyramid.
From the Formula of the Volume of the Pentagonal pyramid, we can derive the formula of the base edge
Therefore, the Formula for the base area of a pentagonal pyramid is =
Volume = 5/12× tan(54°) × height × (Base edge)²
(Base edge)² = Volume ÷ (5/12× tan(54°) × height)
Base edge = √[(Volume ÷ ( 5/12× tan(54°) × height)
In the question, we are given the following values:
Volume = 165.17 cubic meters
Height = 8 meters.
Base edge = √[(165.17m³ ÷ ( 5/12× tan(54°) × 8m)]
Base edge = 6.00008meters(m)
Step 2
The second and final stap would be to find the Base area of the Pentagonal pyramid.
The formula would be :
5/4 × tan(54°) × (base edge)²
The Base area = 5/4 × tan(54°) ×(6.00008m)²
The Base area of the Pentagonal pyramid = 61.94m²