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 (dm²)

S_city = WILL_xq + 2S_dd = 42 + 2 x (4 x 3) = 66 (dm²)

b.

S_xq = (12 + 8) x 2 x 7 = 280 (cm²)

S_city = 280 + 2 x (12 x 8) = 472 (cm²)

c.

\({S_{xq}} = \left( {\frac{5}{7} + \frac{2}{5}} \right)x2x\frac{1}{2} = \frac{{39} }{{35}}x2x\frac{1}{2} = \frac{{39}}{{35}}\) (m²)

\({S_{tp}} = \frac{{39}}{{35}} + 2x\left( {\frac{5}{7}x\frac{2}{5}} \right) = \ frac{{39}}{{35}} + \frac{4}{7} = \frac{{59}}{{35}}\) (m²)

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 5.8m²?

Solution

The area around the room is

(4.2 + 3.6) x 2 x 3.4 = 53.04 (m²)

The ceiling area is

4.2 x 3.6 = 15.12 (m²)

Surrounding area and ceiling area are

53.04 + 15.12 = 68.16 (m²)

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