A manufacturer uses a mold to make a part in the shape of a triangular prism. The dimensions of this part are shown below.
A triangular prism is shown. The height of the prism is 10.75 millimeters. The sides of the triangular base measure 6.5 , 6.5 , and 12.6 millimeters. A line segment extends from the 12.6 millimeter side to the opposite vertex. The segment is labeled 1.6 millimeters. A small square is at the intersection of the segment with the side of the triangle.
Which estimate is closest to the volume in cubic millimeters of the part?
A. 108
B. 217
C. 440
D. 880
The triangular base has area $\frac{1}{2} (6.5)(6.5) = 21.125$ square millimeters. The height of the triangular base can be found using the Pythagorean theorem: $h = \sqrt{6.5^2 - (0.8)^2} = \sqrt{41.69} \approx 6.45$ millimeters (rounded to hundredths place).
Therefore, the volume of the triangular prism is $V = Ah = (21.125)(6.45) \approx 136.44$ cubic millimeters. The closest estimate is $\boxed{\textbf{(B)}\ 217}$ cubic millimeters.