*I am assuming that the hexagons in all questions are regular and the triangle in (24) is equilateral*
(21)
Area of a Regular Hexagon: 
square units
(22)
Similar to (21)
Area = 
square units
(23)
For this case, we will have to consider the relation between the side and inradius of the hexagon. Since, a hexagon is basically a combination of six equilateral triangles, the inradius of the hexagon is basically the altitude of one of the six equilateral triangles. The relation between altitude of an equilateral triangle and its side is given by:
Hence, area of the hexagon will be: 
square units
(24)
Given is the inradius of an equilateral triangle.
Substituting the value of inradius and calculating the length of the side of the equilateral triangle:
Side = 16 units
Area of equilateral triangle = 
square units
105 - 75 = 30 That should do it.
Answer revealed in the attachment below.
Similar triangles may or may not have equal measures
Allie's error is that Allie did not state the similarity theorem
<h3>How to determine
Allie's error </h3>
The statement JKL ~ XYZ means that:
Triangles JKL and XYZ are similar triangles
From the complete question, we have the following highlights:
- Angles J and X have equal measures of 55 degrees
- The side lengths of triangle XYZ are 3 multiplied by the corresponding side lengths of triangle JKL
The above means that, both triangles are similar by SAS or SSS
In Allie's statement, the similarity theorem is not stated
Hence, Allie's error is that Allie did not state the similarity theorem
Read more about similar triangles at:
brainly.com/question/14285697
Answer:
x=(-6)
Step-by-step explanation:
