Practice calculating the total and surrounding area of a rectangular box

### 1.1. Solving exercises in the textbook Practice page 110

**Lesson 1 Textbook page 110**

Calculate the perimeter and total area of a rectangular box with:

a) Length 25dm, width 1.5m and height 18dm.

b) Length \(\frac{4}{5}\)m, width \(\frac{1}{3}\)m and height \(\frac{1}{4}\)m.

__Solution guide:__

a) Convert 1.5m = 15dm

The area around the rectangular box is:

(25 + 15) × 2 × 18 = 1440 (dm^{2})

The area of the base of the rectangular box is:

25 × 15 = 375 (dm^{2})

The total area of the rectangular box is:

1440 + 375 × 2 = 2190 (dm^{2})

b) The perimeter of the rectangular box is:

\(\left( {\frac{4}{5} + \frac{1}{3}} \right) \times 2 \times \frac{1}{4} = \frac{{17}}{{ 30}}\left( {{m^2}} \right)\)

The area of the base of the rectangular box is:

\(\frac{4}{5} \times \frac{1}{3} = \frac{4}{{15}}\left( {{m^2}} \right)\)

The total area of the rectangular box is:

\(\frac{{17}}{{30}} + \frac{4}{{15}} \times 2 = \frac{{11}}{{10}}\left( {{m^2}) } \right)\)

Answer: a) 1440dm^{2} ; 2190dm^{2}

b) \(\frac{{17}}{{30}}{m^2};\frac{{11}}{{10}}{m^2}\)

Lesson 2 Textbook page 110

A rectangular box without lid has a length of 1.5m, a width of 0.6m and a height of 8dm. The outside of the barrel is painted. How many square meters is the painted area?

__Solution guide:__

Convert: 8dm = 0.8m

The surrounding area of the crate is:

(1.5 + 0.6) × 2 × 0.8 = 3.36(m .)^{2})

The area of the bottom of the crate is:

1.5 × 0.6 = 0.9(m^{2})

Painted area is:

3.36 + 0.9 = 4.26(m^{2})

Answer: 4.26m^{2}

Lesson 3 Textbook page 110

Correct write D, false write S.

a) The total areas of the two rectangles are equal.

b) The total areas of the two rectangles are not equal.

c) The perimeters of the two rectangles are equal.

d) Surrounding areas of two rectangular boxes are not equal.

__Solution guide:__

+) Picture on the left:

The area × around the rectangular box is:

(2.5 + 1.5) × 2 × 1.2 = 9.6 (dm^{2})

The area of the base of the rectangular box is:

2.5 × 1.5 = 3.75 (dm2)

The total area of the rectangular box is:

9.6 + 3.75 × 2 = 17.1(dm2)

+) Picture on the right

The area × around the rectangular box is:

(1.5 + 1.2) × 2 × 2.5 = 13.5 (dm2)

The area of the base of the rectangular box is:

1.5 × 1.2 = 1.8(dm2)

The total area of the rectangular box is:

13.5 + 1.8 × 2 = 17.1 (dm2)

We have: 9.6dm2 < 13.5dm2, deduce the area × around of the two rectangular boxes are not equal.

17.1(dm2) = 17.1(dm2) , infer that the total area of the two rectangular boxes is equal.

So we have the following result:

a) Yes b) S c) S d) RED

Note: Two given rectangles are equal but placed in two different positions, so they have the same total area but different surrounding × area.

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