Perimeter of Polygons

Show your work for each problem.

1.
What is the perimeter of a rectangle with length 6 cm and width 4 cm?
1. a)10 cm
2. b)12 cm
3. c)20 cm
4. d)24 cm
Answer: 20 cm
cm, or cm. The rectangle has two sides of 6 cm and two sides of 4 cm.
2.
A triangle has sides of 5 m, 7 m, and 8 m. What is its perimeter?
1. a)40 m
2. b)20 m
3. c)12 m
4. d)15 m
Answer: 20 m
m. The perimeter is the sum of all three sides.
3.
A square has sides of 9 cm each. What is its perimeter?
Answer: 36
cm. A square has 4 equal sides, so we multiply the side length by 4.
4.
What is the perimeter of a rectangle with length 10 m and width 3 m?
Answer: 26
m, or m.
5.
Which formula correctly calculates the perimeter of a rectangle?
1. a)
2. b)
3. c)
4. d)
Answer:
adds both lengths and both widths. gives area, not perimeter!
6.
A regular pentagon has sides of 7 cm each. What is its perimeter?
Answer: 35
cm. A pentagon has 5 equal sides, each 7 cm long.
7.
A regular hexagon has a perimeter of 48 cm. What is the length of each side?
1. a)4 cm
2. b)8 cm
3. c)6 cm
4. d)12 cm
Answer: 8 cm
Side = cm. Since all 6 sides are equal, we divide the total perimeter by 6.
8.
A rectangle has a perimeter of 34 cm and a length of 11 cm. What is its width?
Answer: 6
, so , then , and cm.
9.
Find the perimeter of a rectangle with length 15 m and width 8 m.
Answer: 46
1. What is the length of the rectangle? 15
2. What is the width of the rectangle? 8
3. Add the length and width: 23
4. Multiply by 2 to get the perimeter: 46
10.
A garden is shaped like a regular octagon with each side measuring 5 m. How much fencing is needed to surround it?
Answer: 40
1. How many sides does an octagon have? 8
2. What is the length of each side? 5
3. Multiply: 40
11.
A quadrilateral has sides of 6 cm, 9 cm, 7 cm, and 10 cm. What is its perimeter?
Answer: 32
1. How many sides does a quadrilateral have? 4
2. Add the first two sides: 15
3. Add the third side: 22
4. Add the fourth side: 32
12.
A rectangle has a perimeter of 50 m. If the length is 3 times the width, what is the width?
Answer: 6.25
Let width = , length = . . So m.
13.
A rectangular garden is 20 m long. If 68 m of fencing surrounds it completely, what is the garden's width?
Answer: 14
1. What is the perimeter of the garden? 68
2. Write the formula: . What is ? 40
3. Substitute: . What is ? 28
4. Solve: . What is ? 14
14.
An equilateral triangle and a square have the same perimeter. If the triangle has sides of 12 cm, what is the side length of the square?
Answer: 9
1. How many sides does an equilateral triangle have? 3
2. Find the triangle's perimeter: 36
3. The square has the same perimeter. How many sides does a square have? 4
4. Find the square's side: 9
15.
A picture frame is 25 cm by 35 cm. How much wood is needed for the frame?
1. a)60 cm
2. b)120 cm
3. c)70 cm
4. d)875 cm
Answer: 120 cm
cm. The 875 cm answer comes from multiplying (area), which is wrong for this problem!
16.
A farmer has 100 m of fencing. He wants to build a rectangular pen with maximum area. If the length is 25 m, what is the width?
Answer: 25
1. What is the total perimeter (fencing)? 100
2. Write the formula . What is ? 50
3. Substitute: . What is ? 50
4. Solve: . What is ? 25