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Segment EF is the midsegment of trapezoid ABCD. Find the length of segment EF if segment AB is 20 and segment CD is 12.

Segment EF is the midsegment of trapezoid ABCD Find the length of segment EF if segment AB is 20 and segment CD is 12 class=

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choixongdong

Midsegment = 1/2(base1 + base2)

EF = 1/2(AB + CD)

EF = 1/2(20 + 12)

EF = 1/2(32)

EF = 16

Answer

EF = 16

LudwigGR

Answer:

The length of the mid-segment EF is 16.

Step-by-step explanation:

In this exercise the main idea is to know the formula for the mid-segment of a trapezoid. This formula should be well known because it is used to find the area of a trapezoid.

If we denote the mid-segment of a trapezoid as [tex]m[/tex], the larger basis as [tex]B[/tex] and the smaller basis as [tex]b[/tex], the formula states:

[tex]m = \frac{B+b}{2}.[/tex]

In this particular exercise [tex]m=EF[/tex], [tex]B=AB[/tex] and [tex]b=DC[/tex].

Thus,

[tex]EF = \frac{DC + AB}{2} = \frac{20+12}{2} = \frac{32}{2} = 16.[/tex]

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