Question

both figures are regular pentagons. what is the perimeter of figure b?
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a. 32 ft
b. 35 ft
c. 38 ft
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Explanation:

Step1: Recall the formula for the perimeter of a regular pentagon

The perimeter \(P\) of a regular pentagon is \(P = 5s\), where \(s\) is the length of a side.

Step2: Find the side - length relationship

Since both are regular pentagons, assume the side - length of figure \(A\) is \(s_{A}=7\) ft. Let the side - length of figure \(B\) be \(s_{B}\). If we assume a scale - factor relationship (not given explicitly, but common in such problems, and since it's a multiple - choice with options, we can check the ratio). If we assume a simple arithmetic or proportional relationship. Let's check each option:

• For option \(a\): If \(P = 32\) ft, then \(s=\frac{32}{5}=6.4\) (not an integer, and no indication of non - integer side from figure \(A\)'s \(s = 7\) which is integer).
• For option \(b\): If \(P = 35\) ft, then \(s=\frac{35}{5}=7\) ft. But if figure \(A\) has \(s = 7\) ft, and they are two different figures (assuming non - congruent as they are separate in the problem), this is less likely.
• For option \(c\): If \(P = 38\) ft, \(s=\frac{38}{5}=7.6\) (non - integer). Wait, no, we made a wrong approach. Wait, actually, looking at the multiple - choice options and the fact that it's a basic perimeter problem for a regular pentagon (a 5 - sided polygon with equal sides). If we assume that maybe there was a mis - draw and it's a typo, but more likely, if we consider that for a regular pentagon perimeter \(P = 5s\). If we assume that the problem might have a side - length for figure \(B\) such that \(P=35\) (since \(35 = 5\times7\), but if we consider another approach: maybe it's a mis - labeled problem and it's a regular heptagon (7 - sided polygon, perimeter \(P=7s\)). But no, the problem says pentagon. Wait, re - checking: if it's a pentagon (5 sides). If we assume that the side - length of figure \(B\) is \(7\) (same as figure \(A\), but no, the problem shows two different figures. Wait, no, wait the options: the perimeter of a regular pentagon \(P = 5s\). If we assume that the side - length of figure \(A\) is \(7\) (given as \(7\) ft in the figure \(A\) label). If the problem is in error (maybe a heptagon, but no). Wait, no, another approach: count the number of sides (5 for pentagon). If we assume that the problem is a simple perimeter calculation and there was a mis - print. Wait, no, looking at the options: \(35=5\times7\). Maybe the problem intended to say that figure \(B\) has the same side - length as figure \(A\) (even though they are drawn as separate, but in a basic problem for a beginner, they might assume that.

Answer:

B. \(35\) ft