Mini Project 7 Similar Polygons
1. Find the perimeter and area of each of the following polygons.
a.
b.
c.
d.
X
G
A
D
5
4
B
3
10
8
C
Perimeter = _____
Area = _____
Y
6
8
Z
Perimeter = _____
Area = _____
E
T
W
24
5
F
Perimeter = _____
Area = _____
2. a.
b.
c.
d.
Are ΔABC and ΔXYZ similar? YES
NO
What is the ratio of the corresponding sides?
What is the ratio of the perimeters?
What is the ratio of the areas?
_____
_____
_____
3. a.
b.
c.
d.
Are DEFG and TUVW similar? YES
NO
What is the ratio of the corresponding sides?
What is the ratio of the perimeters?
What is the ratio of the areas?
_____
_____
_____
U
15
V
Perimeter = _____
Area = _____
4. a. How does the ratio of the sides compare to the ratio of the perimeters?
______________________________________________________________________________
b. How does the ratio of the sides compare to the ratio of the areas?
______________________________________________________________________________
5. If the similarity ratio of two similar figures is a/b, then the ratio of their perimeters is _____ and
the ratio of their areas is _____.
Use the conjecture you have established in #5 to work each of the following problems.
1. The ratio of the perimeter of ΔABC to the perimeter of ΔDEF is 8/9. What is the similarity ratio of
ΔABC to ΔDEF?
__________
2. The ratio of the area of ΔABC to the area of ΔDEF is 16/25. What is the similarity ratio of ΔABC to
ΔDEF?
__________
3. Given that rectangle ABCD ~ EFGH. The area of rectangle ABCD is 135 in2. The area of rectangle
EFGH is 240 in2. If the width of rectangle ABCD is 9 in., what is the length and width of rectangle
EFGH? Show your work.
__________ 4. ΔABC ~ ΔRST, and the area of ΔABC is 24m2. What is the area of ΔRST?
Show your work.
A. 16m2
B. 29 m2
2
C. 36 m
D. 54 m2
__________ 5. The similarity ratio of two similar pentagons is 9/4. What is the ratio of the perimeters
of the pentagons?
A. 2/3
B. 3/2
C. 9/4
D. 81/16
__________ 6. Of two similar triangles, the second triangle has sides half the length of the first. Given
that the area of the first triangle is 16 ft2, find the area of the second.
Show your work.
A. 4 ft2
B. 8 ft2
C. 16 ft2
D. 32 ft2