1) Given the regular octagon \(ABCDEFGH\) and \(\angle 1, \angle 2, \angle 3, \angle 4, \angle 5\) and \(\angle 6\) as shown:
a) What is the sum of the measures of the interior angles of this octagon? b) What is the sum of the measures of the exterior angles of this octagon? c) What is the NAME of \(\angle 1\), or \(\angle BKC\). That is, what do we call the angle as it relates to the octagon? d) What is the \(m\angle 1\)? e) What is the \(m\angle 2\)? f) What is the \(m\angle 3\)? g) What is the \(m\angle 4\)? h) What is the NAME of \(\angle 5\)? i) What is the \(m\angle 5\)? j) What is the NAME of \(\angle 6\)? k) What is the \(m\angle 6\)? l) Name a segment that is a radius? m) Name a segment that is an apothem? |
2) Let’s try it again but this time with regular hexagon \(ABCDEF\) and \(\angle 1, \angle 2, \angle 3, \angle 4, \angle 5\) and \(\angle 6\) as shown:
a) What is the sum of the measures of the interior angles of this hexagon? b) What is the sum of the measures of the exterior angles of this hexagon? c) What is the NAME of \(\angle 1\), or \(\angle BKC\). That is, what do we call the angle as it relates to the hexagon? d) What is the \(m\angle 1\)? e) What is the \(m\angle 2\)? f) What is the \(m\angle 3\)? g) What is the \(m\angle 4\)? h) What is the NAME of \(angle 5\)? i) What is the \(m\angle 5\)? j) What is the NAME of \(\angle 6\)? k) What is the \(m\angle 6\)? l) Name a segment that is a radius? m) Name a segment that is an apothem? |
4) What is the measure of a central angle of a regular decagon?
7) What is the length of a side of a regular triangle given an apothem length of \(\sqrt{3}\)?
8) What is perimeter of a square given a radius length of \(7\sqrt{2}\)?
8) What is perimeter of a square given a radius length of \(7\sqrt{2}\)?
9) A regular octagon with \(A (0, 0)\) and \(B (10, 0)\). Point \(K\) is the center of the figure. Verify that point \(K\) is located at \(( 5, 5+5\sqrt{2} )\)
10) What is the area of regular figure above?
11) What is the area of regular hexagon with a side length of \(6\) cm?
11) What is the area of regular hexagon with a side length of \(6\) cm?
13) What is the area of a regular dodecagon given a perimeter of \(66\) in\(^2\).
14) Find the length of side of a regular nonagon with an area of approximately \(285.85\) m\(^2\).
14) Find the length of side of a regular nonagon with an area of approximately \(285.85\) m\(^2\).
15) Below is a partial figure of a regular polygon with a side length of \(4.6\) cm and an apothem of \(7.079\) cm. If the area of the regular is approximately \(162.3\) cm\(^2\), then how many sides does the polygon have?
16) Find the area of an equilateral triangle with a perimeter of \(300\) feet.
17) Find the area of a square with a perimeter of \(300\) feet.
18) Find the area of a regular pentagon with a perimeter of \(300\) feet.
19) Find the area of a regular hexagon with a perimeter of \(300\) feet.
20) Find the area of a regular octagon with a perimeter of \(300\) feet.
21) For #16-20, name a figure that would have the most area with a given perimeter of \(300\) feet.
Solution Bank
17) Find the area of a square with a perimeter of \(300\) feet.
18) Find the area of a regular pentagon with a perimeter of \(300\) feet.
19) Find the area of a regular hexagon with a perimeter of \(300\) feet.
20) Find the area of a regular octagon with a perimeter of \(300\) feet.
21) For #16-20, name a figure that would have the most area with a given perimeter of \(300\) feet.
Solution Bank