FIND The Height 6. triangular pyramid: volume \( 270 \mathrm{~cm}^{3} \); base edge 15 cm ; height of base 4 cm

To find the height of a triangular pyramid, we can use the volume formula: \( V = \frac{1}{3} \times B \times h \), where \( B \) is the area of the base and \( h \) is the height of the pyramid. The area of the base, which is triangular, can be calculated using the formula \( B = \frac{1}{2} \times \text{base} \times \text{height} \). Given the base edge is 15 cm and the height of the base is 4 cm, the area will be \( B = \frac{1}{2} \times 15 \times 4 = 30 \mathrm{~cm}^{2} \). Now we substitute the values into the volume equation: \( 270 = \frac{1}{3} \times 30 \times h \). Solving for \( h \), we get \( h = \frac{270 \times 3}{30} = 27 \) cm. Therefore, the height of the triangular pyramid is 27 cm!