Question

3 pts
Question 1
You find a crystal in the shape of a prism. Find the volume of the crystal.
The point Bis directly underneath point E, and the following lengths are known:
• From A to B: 2 mm
• From B to C:3 mm
. From A to F: 6 mm
• From B to E: 10 mm
. From C to D: 7 mm
• From A to G: 4 mm
G
А
B
What is the area of the base? ( 1 point) Explain or show your reasoning. (2 points)

Answer 1

The Volume of crystals is 160 mm³ while the area of the base is 20 mm².

Volume

Volume is the amount of space occupied by a three dimensional shape or object.

Area of triangle = (1/2) * DF * height

Height = 10 - 6 = 4 mm, DF = AC = AB + BC = 2 + 3 = 5 mm

Area of triangle = (1/2) * 5 * 4 = 10 mm²

Volume of triangle prism = Area of triangle * AG = 10 * 4 = 40 mm³

Volume of rectangular prism = A to F * AC * AG = 6 * 5 * 4 = 120 mm³

Volume of crystals = 120 + 40 = 160 mm³

Area of base = AC * AG = 5 * 4 = 20 mm²

The Volume of crystals is 160 mm³ while the area of the base is 20 mm².

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