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Last Name:________________________________ Grade: _______
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Perimeter
In this math challenge, we will be solving problems involving a specific term called perimeter.
Perimeter is the distance around a 2-dimensional object. You find the perimeter of a shape by
adding the lengths of the sides. For example, a square has four sides. To determine the perimeter
of this square, just add the four sides together. Since every side of a square is the same, the
perimeter is: 4 inches + 4 inches + 4 inches + 4 inches = 16 inches.
Kinder & First Grade: solve at least 3 problems.
Second & Third Grade: solve at least 6 problems.
Fourth Grade and above: solve at least 12 problems.
Problems
Answer
1.
What is the perimeter of a square with side length of 6 cm? Express your answer in cm.
24 [cm]
2.
An equalateral triangle is a triangle in which all three sides are equal. Lisa drew an
equilateral triangle that measured 3 inches on each side. What is the perimeter of the
triangle that she drew?
9 [in]
3.
Laura’s bedroom shape is a square. The side's length is 11 feet long. What is the perimeter
of her bedroom?
44 [ft]
4.
A rectangular room is 12 feet long and 9 feet wide. Find its perimeter in feet.
42 [ft]
5.
Shota’s room is in a shape of a regular hexagon (how cool that is!). The perimeter of his
room is 78 feet. Find the length of each side.
13 [ft]
6.
Ender measured the perimeter of his rectangular bedroom. If the perimeter is 46 feet and
its length is 14 feet, what is the measurement of the width of his bedroom?
9 [ft]
7.
Justin cut a piece of square paper with side length 5 cm.
Elizabeth cut a piece of rectangular paper that is 8 cm long
and 6 cm wide. They put together their papers to make the
shape as the figure on the right. What is the perimeter of the
figure?
38 [cm]
8.
6 cm
5 cm
8 cm
A piece of square paper with side length 18 cm was cut into half as in the
picture. What is the perimeter of each new piece of paper?
54 [cm]
The new piece of paper: 16 cm by 8 cm. The perimeter is (18 + 9) x 2 = 54 cm.
9.
The figure below is made up of 3 identical squares. Each side of the square
measures 6 inches. What is the perimeter of the figure?
48 [cm]
2016-2017 Math Challenge
10. What is the perimeter of the figure below? All angles in the figure are right angles.
Hint: do not estimate.
52 [cm]
9 cm
17 cm
11. The length of a dining room is 8 feet longer than its width. If its perimeter is 84 feet. What
is the measurement of the dining room? Hint: Draw a model.
25 ft. by 17 ft.
8 ft.
Length:
84/2 = 42 ft.
Width:
2 units  42 + 8 = 50, so 1 unit (length): 50/2 = 25 feet. Width of the room: 25 – 8 = 17 feet. The room’s
measurement is 25 ft. by 17 ft.
12. A large square paper was cut into half, then the results were cut again into half for a few
more times. If at the end of cutting, there were 64 small squares, and each square has a
side of 3 inches long, what is the perimeter of the large square paper?
96 [inches]
Since there are 64 small squares, the original side of the square must be: 8 x 3 inches: 24 inches. Thus, the
perimeter is 24 x 4 = 96 inches.
13. Neha’s bedroom is 12 feet long and 9 feet wide. She wants to put a border along the top
of all four walls of the bedroom. The border is sold in two yard packs. What is the least
number of packs Neha can buy to have enough border to decorate her bedroom?
7 [packs]
Perimeter: 12 + 9 + 12 + 9 = 42 feet. The least number of packs Neha can buy is 7 packs.
14. The figure on the right is made up of a square, a circle, and 2
identical semicircles. Find the perimeter of the shaded parts in the
figure below. Use 𝜋 = 3.14.
157 [inches]
Perimeter of the shaded parts = Circumference of a circle = 3.14 x 50 = 157 inches
50 inches
15. The figure on the right is made up of a rectangle and a
triangle. What is the perimeter of the figure?
Hint: Find the missing length.
Missing length: 𝑐 2 = 𝑎2 + 𝑏2 → 𝑐 2 = 122 + (30 − 25)2 =
25 in.
80 [inches]
12 in.
144 + 25 = 169. 𝑐 = √169 = 13. Perimeter: 12+25+13+30= 80 inches.
30 in.
16. The figure on the right is made up of 3 squares and a semicircle with a
diameter of 36 inches. The dot in the middle is the center of the
semicircle. Find the perimeter of the entire figure. Use 𝜋 = 3.14.
128.52 [inches]
The perimeter of the figure is 4 times the length of the biggest square plus the length of
the arc. Length of the biggest square is 18 inches. The perimeter: 18 x 4 + ½ x 3.14 x 36 =
128.52 in.
2016-2017 Math Challenge