1. **State the problem:** Calculate the volume of a shape made from a triangular prism with a rectangular hole through the middle. 2. **Identify the dimensions:** - Triangular prism base triangle: base $b = 15$ cm, height $h = 14$ cm - Prism depth (length) $L = 6$ cm - Rectangular hole dimensions: width $w = 4$ cm, height $h_r = 3$ cm, depth same as prism $L = 6$ cm 3. **Formula for volume of a triangular prism:** $$ V_{prism} = \text{area of triangle} \times \text{length} = \frac{1}{2} b h \times L $$ 4. **Calculate volume of the triangular prism:** $$ V_{prism} = \frac{1}{2} \times 15 \times 14 \times 6 $$ $$ = \frac{1}{2} \times 15 \times 14 \times 6 $$ $$ = 7.5 \times 14 \times 6 $$ $$ = 7.5 \times 84 $$ $$ = 630 \text{ cm}^3 $$ 5. **Formula for volume of rectangular hole:** $$ V_{hole} = w \times h_r \times L $$ 6. **Calculate volume of the rectangular hole:** $$ V_{hole} = 4 \times 3 \times 6 = 72 \text{ cm}^3 $$ 7. **Calculate volume of the shape:** $$ V_{shape} = V_{prism} - V_{hole} = 630 - 72 = 558 \text{ cm}^3 $$ **Final answer:** The volume of the shape is $558$ cubic centimeters.