To name each figure below, use as many of the letters A, B, C,...as you need, in order, starting with A. For each figure, how many letters do you need? With this labeling, how many different ways can you name the figure?
a. a triangle b. a quadrilateral c. a pentagon
To name each figure, you need to use as many letters as there are sides in the figure.
a. For a triangle, you need to use 3 letters because a triangle has 3 sides. So the first figure would be labeled with the letter A, the second with A and B, and the third with A, B, and C.
b. For a quadrilateral, you need to use 4 letters because a quadrilateral has 4 sides. So the first figure would be labeled with the letter A, the second with A and B, the third with A, B, and C, and the fourth with A, B, C, and D.
c. For a pentagon, you need to use 5 letters because a pentagon has 5 sides. So the first figure would be labeled with the letter A, the second with A and B, the third with A, B, and C, the fourth with A, B, C, and D, and the fifth with A, B, C, D, and E.
To determine the number of different ways you can name the figure, you simply need to count the number of possible combinations of letters for each figure.
For the first figure (triangle), there are 3 possible combinations of letters (A, AB, ABC).
For the second figure (quadrilateral), there are 4 possible combinations of letters (A, AB, ABC, ABCD).
For the third figure (pentagon), there are 5 possible combinations of letters (A, AB, ABC, ABCD, ABCDE).
Therefore, the number of different ways you can name the figures are:
a. Triangle: 3
b. Quadrilateral: 4
c. Pentagon: 5.