Rectangular box, cube

### 1.1. Knowledge to remember

**a) Rectangle**

Match box

Bricks

Rectangular

Matchboxes and bricks are rectangular in shape.

A rectangular box has 6 faces (as shown in the figure): two bottom faces (face 1 and face 2) and four sides (face 3, face 4, face 5 and face 6) are rectangles. Side 1 and side 2; side 3 and side 5; side 4 and side 6.

Rectangular

The rectangular box (right image) has:

– The vertex centers are: vertex A, vertex B, vertex C, vertex D, vertex M, vertex N, vertex P, vertex Q.

– The twelve edges are: side AB, edge BC, edge DC, edge AD, edge MN, edge NP, edge QP, edge MQ, edge AM, edge BN, edge CP, edge DQ.

The rectangular box has three dimensions: length, width, and height.

**b) Cube**

We also often encounter in practice some objects such as dice having the shape of a cube.

A cube has six faces that are equal squares,

### 1.2. Solve textbook exercises page 108

**Lesson 1 Textbook page 108**

Write the correct number in the blank:

*Solution guide:*

Based on the theory of rectangular boxes and cubes, we have the following results:

Lesson 2 Textbook page 108

a) Show the equal sides of the rectangular box (right figure).

b) Know that a rectangular box has length 6cm, width 3cm, height 4cm. Calculate the area of the bottom surface of MNPQ and the side faces ABNM, BCPN.

*Solution guide:*

a) The equal sides of the rectangular box are:

AB = CD = MN = PQ

AD = BC = MQ = NP

AM = BN = CP = DQ

b) The area of the bottom surface of MNPQ is:

6 x 3 = 18 (cm^{2})

The area of the side surface ABNM is:

6 x 4 = 24 (cm^{2})

The area of the side surface BCPN is:

4 x 3 = 12 (cm^{2})

Answer: b) MNPQ bottom surface: 18cm^{2}

ABNM bottom surface: 24cm^{2}

BCPN bottom: 12cm^{2}

Lesson 3 Textbook page 108

Which of the following figures is a rectangular box and which is a cube?

*Solution guide:*

- Figure A is a rectangular box (because there are three dimensions: length, width, height).
- Figure B is neither a rectangle nor a cube.
- Figure C is a cube (because there are 6 faces that are all equal squares).

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