Amanufacturer uses a mold to make a part in the shape of a triangular prism. the dimensions of this part are shown below.

which estimate is closest to the volume in cubic millimeters of the part?

a. 65
b. 125
c. 249
d. 446

  B. 125

Step-by-step explanation:

If you compute the actual volume as the product of the area of the triangle and the length of the piece, you get ...

  V = Bh = (1/2)(14.4 mm)(2.1 mm)·(8.25 mm) = 124.74 mm

That is closest to choice B, 125 mm.

___

You can estimate the volume by rounding the dimensions. The triangle can be considered to be a rectangle of the same base width and half the height, so you are looking to estimate the product ...

  (8.25 mm)(14.4 mm)(1.05 mm)

That's about 8 × 15 × 1 = 120 . . . . mm³.

Certainly, this is an estimate sufficiently close to allow you to choose the correct answer.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

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