Final answer:
The height of the hexagonal pyramid is 12.6 meters. The area of a triangle with a base of 166 mm and a height of 930 mm is 0.0772 m² when the values are converted to meters and calculated using the area formula with three significant figures.
Step-by-step explanation:
Height of the Hexagonal Pyramid
To find the height of a hexagonal pyramid given its volume and the area of the base, we can use the formula for the volume of a pyramid: V = (1/3) × base area × height. Plugging in the given values, we have 604.8 m³ = (1/3) × 144 m² × height. By isolating the height, we find that height = (3 × 604.8 m³) / 144 m² = 12.6 m. Therefore, the height of the hexagonal pyramid is 12.6 meters.
Area of the Triangle
To find the area of a triangle, we use the formula area = 1/2 × base × height. First, we should convert millimeters to meters to maintain consistency: base = 166 mm = 0.166 m, height = 930.0 mm = 0.930 m. Now, by calculating 1/2 × 0.166 m × 0.930 m, we find the area to be 0.07719 m². Since the base and height are given to three significant figures, our final answer should also be to three significant figures: 0.0772 m².