Surrounding area and total area of rectangular box

**Lesson 1:** Calculate the perimeter and total area of a rectangular box of length a, width b, height c whose dimensions are given below.

a. a = 4dm; b = 3dm; c = 2dm

b. a = 12cm; b = 8cm; c = 7cm

c. a = \(\frac{5}{7}\) m; b = \(\frac{2}{5}\) m; c = \(\frac{1}{2}\) m

**Solution**

a.

S_{xq} = (a + b) x 2 xc = (4 + 3) x 3 x 2 = 42 (dm^{2})

S_{city} = WILL_{xq} + 2S_{dd} = 42 + 2 x (4 x 3) = 66 (dm^{2})

b.

S_{xq} = (12 + 8) x 2 x 7 = 280 (cm^{2})

S_{city} = 280 + 2 x (12 x 8) = 472 (cm^{2})

c.

\({S_{xq}} = \left( {\frac{5}{7} + \frac{2}{5}} \right)x2x\frac{1}{2} = \frac{{39} }{{35}}x2x\frac{1}{2} = \frac{{39}}{{35}}\) (m^{2})

\({S_{tp}} = \frac{{39}}{{35}} + 2x\left( {\frac{5}{7}x\frac{2}{5}} \right) = \ frac{{39}}{{35}} + \frac{4}{7} = \frac{{59}}{{35}}\) (m^{2})

**Lesson 2: **A rectangular room is 4.2m long, 3.6m wide and 3.4m high. People want to whitewash the walls and ceiling. How many square meters is the area to be whitewashed, knowing that the total area of the doors is 5.8m^{2}?

**Solution**

The area around the room is

(4.2 + 3.6) x 2 x 3.4 = 53.04 (m^{2})

The ceiling area is

4.2 x 3.6 = 15.12 (m^{2})

Surrounding area and ceiling area are

53.04 + 15.12 = 68.16 (m^{2})

The area to be whitewashed is

48.16 – 5.8 = 42.36 (m^{2})

**Lesson 3: **A bakery factory needs 30,000 cardboard boxes to store cakes. The bottom box is a square with side 25cm and height 6cm. How many square feet of cardboard is needed to make the number of boxes mentioned above, knowing that the folded edges of the box take up about \(\frac{8}{100}\) that area will be the number of square meters of cardboard needed to make the box. cake. Then calculate the area needed to make 30,000 such boxes.

**Solution**

The perimeter of a rectangular box is

(25 x 4) x 6 = 600 (cm^{2})

The total area of a box is

600 + (25 x 25) x 2 = 1850 (cm^{2})

The area of the folded edges is

\(1850{\rm{ }}x\frac{8}{{100}} = 148\) (m^{2})

The area of cardboard to make one box is

1850 + 148 = 1998 (cm^{2})

The number of square meters of cardboard required to make 30,000 boxes of cakes is

1998 x 30 000 = 59 940 000 (cm^{2}) or 5994 m^{2}

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