Final answer:
To calculate the volume of the triangular prism, multiply the base area by the depth. In this case, the volume is 42 cm³.
Step-by-step explanation:
To calculate the volume of a three-dimensional triangular prism, you need to multiply the base area by the height. In this case, the base is a triangle with a base of 7 cm and a height of 4 cm. Using the formula for the area of a triangle, which is ½ * base * height, we can calculate the base area as follows:
Base area = ½ * 7 cm * 4 cm = 14 cm²
Next, we multiply the base area by the depth of the prism, which is 30 mm. Since 1 cm is equal to 10 mm, we need to convert the depth to cm:
Depth = 30 mm / 10 mm/cm = 3 cm
Finally, we multiply the base area (14 cm²) by the depth (3 cm) to find the volume:
Volume = 14 cm² * 3 cm = 42 cm³