Comprehension Check

Homework 1.1

#15. Find the sides of each of the two polygons if the total number of sides of the polygons is 13, and the sum of the number of diagonals of the polygons is 25.
Assume: 8 and 5 D1= (n-3) n=13 D1= (8-3)
D=25 D1= 20 D2= (n-3) D2= (5-3) D2= 5 Answer: The number of sides in each polygon is 8 and 5
#17. What is the name of a regular polygon that has 90 diagonals?
Given: D = 90
Required: Name of regular polygon
D = (n-3) - + 3n + 180 = 0
90 = (n-3) n-15 = 0 n+ 12= 0
180 = – 3n n = 15 n= -12
Answer: PENTADECAGON

#19. Find the number of diagonals of a regular polygon whose interior angle measures 144. Given: I.A = 144
Required: D =? For D
I.A = 144n = 180n – 3 D = (n-3) D =
144 = -36 n = -360 D= (10-3) D = 35
144n = 180 (n-2) n = 10 2D = 10(7)
Answer: D = 35

#21. The ratio of areas between two similar triangles is 1:4. If one side of the smaller triangle is 2 units, find the measure of the corresponding side of the other triangle.
Given:
2 x2 = 1 = 4
Solution: = = 4(4) = = 16 = 4

Answer: = 4 units

#23. A regular hexagon A has the midpoints of its edges joined to form a smaller hexagon B. This process is repeated by joining the midpoints of the edges of hexagon B to get a third hexagon C. What is the ratio of the area of hexagon C to the area of hexagon A?
Given:

A B C
Required: Ratio of A1 to A3
Solution: = A = =