a box has length 9.0cm width 6.0 and height 10.2cm. find the total surface area of the box and the volume of the box​

Total surface area : 207cm²

Volume : 550.8³

Step-by-step explanation:

Surface area, first need to work out the area of each face.

A box is symmetrical so some faces will be the same.

Area = Base × Height

Top/bottom : 9 × 6 = 54cm²

side/side = 6 × 10.2 = 61.2cm²

Front/Back = 9 × 10.2 = 91.8cm²

Add then all together

54 + 61.2 + 91.8 = 207cm²

Volume = base × height × width

9 × 6 × 10.2 =550.8cm³

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.