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46.2 square inches

Step-by-step explanation:

A parallelogram is a quadrilateral (4 sided closed figure) with 2 pair of parallel sides.

The diagram shown is a parallelogram.

Top and Bottom are parallel lines,

both sides are parallel lines (left and right).

The area for a parallelogram is given by:

Area = Base * Height

In the given figure, the base is clearly given as 4.2 inches

The height (perpendicular distance from base) is given as 11 inches.

So, basically we do not need the 11.7 inches length of side given.

Now, lets compute the area:

Area = base * height = 4.2 * 11 = 46.2 square inches

∠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.