Download 1. Megan uses the shadow of the flagpole to estimate its height. She

Geometry Pre-AP
HW 7.5
Name _____________________________
1. Megan uses the shadow of the flagpole to estimate its height. She stands so that the tip of her shadow
coincides with the tip of the flagpole’s shadow as shown. Megan is 5 feet tall. The distance from the flagpole to
Megan is 28 feet and the distance between the tip of the shadows and Megan is 7 feet. Calculate the height of
the flagpole.
2. Given that pentagon ABCDE ~ pentagon FGHJK, find each of the following.
a. perimeter of pentagon FGHJK
b. area of pentagon FGHKK
3. If five-foot-tall Madeline casts an 84-inch shadow, then how tall is her friend if at the same time his shadow
is one foot shorter than hers?
4. Given  ABC ~  DEF
a. The ratio of the perimeter of  ABC to the perimeter of  DEF is
8
.
9
What is the similarity ratio of  ABC to  DEF? __________
16
.
25
What is the similarity ratio of  ABC to  DEF? __________
b. The ratio of the area of  ABC to the area of  DEF is
4
.
81
What is the ratio of the perimeter of  ABC to the perimeter of  DEF? ____________
c. The ratio of the area of  ABC to the area of  DEF is
5. Juanita, who is 1.82 meters tall, wants to find the height of a tree in her backyard. From the tree’s base, she
walks 12.20 meters along the tree’s shadow until her head is in a position where the tip of her shadow exactly
overlaps the end of the treetop’s shadow. She is now 6.10 meters from the end of the shadows. How tall is the
tree?
6. Given that  PQR ~  WXY, find each ratio.
a.
perimeter of  PQR
perimeter of  WXY
b.
area of  PQR
area of  WXY
c. How does the result in part (a) compare with the result in part (b)?
7. One overcast day, private eye Samantha Diamond needed to calculate the height of a window in a nearby
building. Because there were no shadows cast, she decided to use mirrors. Sam positioned a mirror on the
ground between herself and the building so that when she looked into the mirror while standing upright, she saw
into the window. The mirror was 1.22 meters from her feet and 7.32 meters from the base of the building.
Sam’s eye was 1.82 meters above ground. How high up on the building was the window located?
8. Given that rectangle ABCD ~ EFGH. The area of rectangle ABCD is 135 in 2 . The area of rectangle EFGH is
240 in2. If the width of rectangle ABCD is 9in., what is the length and width of rectangle EFGH? (Hint: It will
help tremendously to draw a picture)
9. The ratio of the perimeter of square ABCD to the perimeter of square EFGH is
4
. Find the side length of
9
each square.
10. Lindsey was checking out UT last weekend and started to wonder how tall the Tower is. She quickly took out
her compact and placed it 102 feet from the base of the Tower so that thru the mirror she could see the top of
the Tower. If Lindsey is 6 feet and she is standing 2 feet from the mirror, how tall is the Tower?