Questions

1) Describe a polygon.

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2) When the sides of a convex polygon are extended as lines, none of the lines fall in the __________ of the polygon.

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3) When a polygon has at least one side that, if extended, lies within the interior of the polygon, it is called a __________ polygon.

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4) Which figure shown below is a polygon? State the letter of the correct answer.

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5) What is the difference between a concave polygon and a convex polygon?

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6) Classify the polygons shown below by answering the following questions: (a) Which of the polygons are convex? (b) Which of the polygons are concave? For both questions, state the letters of the correct answers.

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7) In the pentagon shown below, measure each of the interior angles with a protractor. What is the SUM of the five interior angles?

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8) What is the missing number in the formula about Theorem 28-A shown below?

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9) Apply Theorem 28-A to the pentagon in problem #8. What is the sum of the five angles in any pentagon? If the sum of the angles in problem #8 is not close to the sum determined by the formula in Theorem 28-A, check the measurements and calculations to determine a more accurate answer.

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10) In the pentagon shown below, measure each of the exterior angles with a protractor. What is the SUM of the five exterior angles?

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11) Theorem 28-B: In a convex polygon, the sum of the exterior angles is ______ degrees.

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12) What is the difference between a polygon and a regular polygon?

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13) What is the sum of the interior angles of a (a) square, (b) pentagon, (c) hexagon, (d) octagon, (e) decagon, (f) 100-gon, and (g) 1000-gon?

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14) What is the size of one interior angle of a (a) square, (b) regular pentagon, (c) regular hexagon, (d) regular octagon, (e) regular decagon, (f) regular 100-gon, and (g) regular 1000-gon?

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15) What is the size of one exterior angle of a (a) square, (b) regular pentagon, (c) regular hexagon, (d) regular octagon, (e) regular decagon, (f) regular 100-gon, and (g) regular 1000-gon?

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16) For all of the polygons listed in the chart, the sum of the exterior angles total how many degrees?

a.) 90

b.) 180

c.) 270

d.) 360

17) As the number of sides increases in a regular polygon, what non-polygonal shape does the regular polygon approach?

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18) In the figure shown below, each angle of heptagon DEFGHIJ is expressed in terms of “x”. What is the value of “x”? (Hint: S = 180(7 – 2))

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19) If an exterior angle of a REGULAR polygon measures 24 degrees, how many sides does the polygon have?

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20) What is a tessellation?

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21) Which of the following regular polygons can be used to make a regular tessellation of a plane?

a.) pentagon

b.) hexagon

c.) heptagon

d.) octagon

22) Which of the following regular polygons CANNOT be used to make a regular tessellation of a plane?

a.) equilateral triangle

b.) square

c.) pentagon

d.) hexagon

23) In order for polygonal figures to tessellate a plane, the vertices of the figures must meet so that the angles of the polygons total how many degrees?

a.) 90 degrees

b.) 180 degrees

c.) 270 degrees

d.) 360 degrees

24) What type of tessellation is illustrated in the hive of honeybees?

a.) regular tessellation

b.) semi-regular tessellation

c.) uniform tessellation

25) A square and an equilateral triangle are placed around a regular hexagon so that they alternate and the vertices of the shapes coincide without the shapes overlapping each other. What type of tessellation may be made from this combination of shapes?

a.) regular tessellation

b.) semi-regular tessellation

c.) uniform tessellation

26) What regular polygon could be added at point J so that the group of shapes would make a semi-regular tessellation as they tile a plane?

a.) equilateral triangle

b.) square

c.) regular pentagon

d.) regular hexagon

27) Activity: Create a tessellation. It may be a semi-regular or uniform tessellation. Describe the tessellation.

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28) What is the area of the parallelogram shown below?

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29) If the area of a parallelogram is 1547 square inches, and its height is 36.4 inches, how long is the base?

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30) For parallelogram ABCD shown below, (a) what is the height and (b) what is the area? Express each answer as a decimal rounded to the nearest tenth. (Hint: Recall that a 45-45-90 degree triangle is an isosceles triangle.)

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31) A grounds keeper is planning to refinish the brick in the front of the building. Determine the area that will be refinished based on the information given in the figure below.

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32) Find the area of the figure shown below.

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33) Use the distance formula to answer the following questions: (a) What is the length of CD? and (b) what is the length of AE? Round the answers to the nearest tenth.

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34) What is the area of parallelogram ABCD? Round the answer to the nearest whole number.

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35) What is the total area of the kitchen and living room?

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36) How wide is the space provided for the two closets between the bedrooms? (Assume that the width of each closet is the shorter side of the rectangle representing the closet.)

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37) What is the area of the home excluding the garage? (Do not include the deck.)

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38) What is the area of the triangle?

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39) If the area of a triangle is 39 feet and the base of the triangle is 6 1/2 feet, what is the height?

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40) What is the length of one side of a square with an area of 252 square centimeters? Express the answer to the nearest tenth.

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41) What is the area of the trapezoid shown below?

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42) If the area of a trapezoid is 176 square feet, its height measures 16 feet, and one of its bases measures 7 feet, what is the length of the other base?

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43) What is the area of rhombus ABCD if AC = 23.9 centimeters and DB = 38.1 centimeters? Round the answer to the nearest tenth.

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44) If the area of a rhombus is 189 square millimeters and one its diagonals measures 24 millimeters, what is the length of the other diagonal?

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45) Answer the following questions about quadrilateral JKLM based on the information given below: (a) What is the area of triangle JKL? (b) What is the area of triangle JML? (c) What is the total area of quadrilateral JKLM?

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