Question

1. consider the given cube and the cross section formed by a plane intersecting the cube parallel to its bases.

image of a cube with side length 5.4 cm, and a cross - section parallel to the base

a. a base of the cube is drawn. sketch the cross section and label the side lengths with the appropriate measurements.

image of a square with side length 5.4 cm labeled on all sides

b. is the cross section a scale drawing of the base? if so, determine the scale factor. if not, explain why not.

Explanation:

Step1: Analyze cross section shape

A plane parallel to a cube's base cuts a square congruent to the base.

Step2: Compare cross section and base

Both are squares with side length $5.4$ cm. Scale factor is $\frac{\text{cross section side}}{\text{base side}}$.
<Expression>
$\text{Scale factor} = \frac{5.4}{5.4} = 1$
</Expression>

Answer:

a. The cross section is a square identical to the base:

    5.4 cm
┌───────────┐
│           │ 5.4 cm
│           │
└───────────┘
    5.4 cm

(All four sides are labeled 5.4 cm, matching the base's dimensions.)

b. Yes, the cross section is a scale drawing of the base, with a scale factor of 1. Since the cross section (formed by a plane parallel to the cube's base) is congruent to the base, all corresponding side lengths are equal, giving a scale factor of 1.