Questions: Find the total outside surface area and volume of the solid object. Assume that the base is regular. The total outside surface area is m². (Round to three significant digits.) The volume is m³. (Round to three significant digits.)

△ Find the total outside surface area of the solid object. ○ Calculate the area of one lateral face. ▷ Each lateral face is a triangle, and its area is calculated using \( \frac{1}{2} \times \text{base} \times \text{height} \). ☼ The area of one lateral face is \( \frac{1}{2} \times 5.1 \, \mathrm{m} \times 9.1 \, \mathrm{m} = 23.205 \, \mathrm{m}^2 \). ○ Calculate the total lateral surface area. ▷ Multiply the area of one lateral face by the number of lateral faces (3 for a triangular pyramid). ☼ The total lateral surface area is \( 3 \times 23.205 \, \mathrm{m}^2 = 69.615 \, \mathrm{m}^2 \). Rounded to three significant digits, this is \( 69.6 \, \mathrm{m}^2 \). ✧ The total outside surface area is approximately \( 69.6 \, \mathrm{m}^2 \). △ Find the volume of the solid object. ○ Calculate the base area. ▷ The base is an equilateral triangle, and its area is calculated using \( \frac{\sqrt{3}}{4} \times \text{side}^2 \). ☼ The base area is \( \frac{\sqrt{3}}{4} \times (5.1 \, \mathrm{m})^2 \approx 11.263 \, \mathrm{m}^2 \). ○ Calculate the volume of the pyramid. ▷ The volume of a pyramid is given by \( \frac{1}{3} \times \text{base area} \times \text{height} \). ☼ The volume is \( \frac{1}{3} \times 11.263 \, \mathrm{m}^2 \times 9.1 \, \mathrm{m} \approx 34.132 \, \mathrm{m}^3 \). Rounded to three significant digits, this is \( 34.1 \, \mathrm{m}^3 \). ✧ The volume is approximately \( 34.1 \, \mathrm{m}^3 \). ☺ Total outside surface area ≈ 69.6 m² Volume ≈ 34.1 m³