A gift box is in the shape of a trapezoidal prism with base lengths of7 inches and 5 inches and a height of 4 inches. The height of the gift box is 8 inches. What is the volume of the gift box?

192 in³

Step-by-step explanation:

A trapezoidal prism is a three dimensional solid that has two similar trapezoids at its top and base.The two similar trapezoids are connected by four rectangles connecting the corresponding sides of the two bases.

The Area of the trapezoid at the top or base = 1/2 (a + b)h

Where a and b are the lengths =  7 inches and 5 inches and the height (h) = 4 inches.

Therefore Area of the trapezoid at the top or base = 1/2 (a + b)h = 1/2(7 + 5)4 = 24 in²

The volume of gift box = Area of the trapezoid at the top or base × height of gift box = 24 × 8 = 192 in³

∠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.

step-by-step explanation:

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