AREA/SYMMETRY REVIEW
NAME:___________________________________
For this test, you should know the following:
1) Area formulas for parallelograms, rhombi, kites, rectangles, triangles, circles, trapezoids, and
regular polygons
2) How to calculate perimeter or circumference
3) The relationships between arc measures, arc lengths, circumference, circle area, and sector
areas
4) Line symmetry and rotational symmetry
5) The relationship between a triangle inscribed in a circle and the circumcenter of the triangle
6) The relationship between a triangle circumscribed about a circle and the incenter of the triangle
7) Be able to answer any problem types from homework and class work during this unit.
8) Working definitions of “central angle of polygon”, “semiperimeter”, “height”, “inscribed”,
“circumscribed”, and “apothem”
9) Using algebra and words (not a formal proof), be able to derive
a) the regular-polygon area formula from a triangle area formula
b) a triangle area formula from the parallelogram area formula
c) the trapezoid area formula from a triangle area formula
Review Problems:
1) In terms of regular polygons, which three values equal
360ᵒ
,
𝑛
where 𝑛 is the number of sides?
2) How do you know that an inscribed equilateral polygon must be regular?
3) For an 𝑛-gon; as 𝑛 → ∞, what happens to the apothem, perimeter, and area? Show work for
“area” part.
4) Given that an apothem is perpendicular to a side of a regular polygon, how do you know that
the apothem bisects the chord, and vice versa?
5) What is true of the six adjacent triangles formed by the diagonals of a regular hexagon?
6) When calculating the area of a regular polygon, why is it more annoying if Mr. Walker gives you
the radius instead of the apothem, side length, or perimeter?
7) Given a length or perimeter of a regular polygon; for which three kinds of regular polygons can
one find exact area measures?
8) What two ways does one have to show that the height of an equilateral triangle is three times
greater (longer) than the apothem?
9) What four additional names can be applied to the center of an equilateral triangle? Explain.
10) How many lines of symmetry does each of these figures have? Show with diagrams.
a) Non-square rectangle
b) Non-square rhombus
c) Equilateral triangle
d) Concave equilateral decagon (star)
e) Regular hexagon
11) State the rotational symmetry for each.
a) Non-square rectangle
b) Non-square rhombus
c) Equilateral triangle
d) Concave equilateral decagon (star)
e) Regular hexagon
12) For regular polygons, what is the difference between lines of symmetry is there is an odd
number of sides versus if there is an even number of sides?
13) The perimeter of Hexagon ABCDEF is 102 inches. A side of Hexagon GHIJKL is 25.5 inches long.
If both hexagons are regular, find:
a) the exact area of each hexagon
b) the ratio of the perimeter of ABCDEF to the perimeter of GHIJKL
c) the ratio of the area of ABCDEF to the area of GHIJKL
14) A regular polygon with a perimeter of 20 feet and an apothem of approximately 2.75 feet is
what type of polygon?
15) Find the approximate apothem and side length of a regular hexagon of area 1000 square feet.
16) The area of a regular pentagon inscribed in a circle is what fraction of the area of the circle?