Answer Keys: Perimeter & Area

Student Concept Worksheet Answers

1

Perimeter = 32 cm, Area = 60 sq cm

P = 2(10) + 2(6) = 20 + 12 = 32 cm | A = 10 x 6 = 60 sq cm

2

Length = 9 meters

P = 2l + 2w, so 28 = 2l + 2(5) = 2l + 10. Then 18 = 2l, so l = 9 m

3

Width = 7 feet

A = l x w, so 56 = 8 x w. Then w = 56 / 8 = 7 ft

4

40 inches

Border goes AROUND = perimeter. P = 2(12) + 2(8) = 24 + 16 = 40 inches

Practice Worksheet Answers

Part A: Find the Perimeter

#	Dimensions	Answer	Work
1	8 cm x 5 cm	26 cm	2(8) + 2(5) = 16 + 10
2	12 m x 7 m	38 m	2(12) + 2(7) = 24 + 14
3	15 ft x 9 ft	48 ft	2(15) + 2(9) = 30 + 18
4	20 in x 11 in	62 in	2(20) + 2(11) = 40 + 22

Part B: Find the Area

#	Dimensions	Answer	Work
5	9 cm x 6 cm	54 sq cm	9 x 6 = 54
6	11 m x 8 m	88 sq m	11 x 8 = 88
7	14 ft x 5 ft	70 sq ft	14 x 5 = 70
8	25 in x 4 in	100 sq in	25 x 4 = 100

Part C: Find Both Perimeter AND Area

#	Dimensions	Perimeter	Area
9	7 m x 4 m	22 m	28 sq m
10	12 ft x 5 ft	34 ft	60 sq ft
11	10 cm x 6 cm	32 cm	60 sq cm
12	15 in x 9 in	48 in	135 sq in

Part D: Find the Missing Side Length

#	Given	Answer	Work
13	P = 24 cm, l = 8 cm	w = 4 cm	24 = 2(8) + 2w; 24 = 16 + 2w; 8 = 2w
14	P = 36 m, w = 7 m	l = 11 m	36 = 2l + 2(7); 36 = 2l + 14; 22 = 2l
15	A = 48 sq ft, l = 8 ft	w = 6 ft	48 = 8 x w; w = 48 / 8
16	A = 72 sq in, w = 6 in	l = 12 in	72 = l x 6; l = 72 / 6

Part E: Word Problems

17

60 feet of fencing

Fencing = perimeter. P = 2(18) + 2(12) = 36 + 24 = 60 ft

18

12 square feet of fabric

Covering = area. A = 4 x 3 = 12 sq ft

19

10 meters

50 = 2(15) + 2w; 50 = 30 + 2w; 20 = 2w; w = 10 m

20

12 feet wide

180 = 15 x w; w = 180 / 15 = 12 ft

21

6,000 square meters

A = 100 x 60 = 6,000 sq m

22

38 inches of ribbon

Ribbon around = perimeter. P = 2(11) + 2(8) = 22 + 16 = 38 in

Challenge Questions:

#23: Rectangle A: 6 x 4 = 24 sq cm. Rectangle B: 7 x 3 = 21 sq cm. Rectangle A has the greater area. (Same perimeter can give different areas!)

#24: Rectangle perimeter = 2(10) + 2(6) = 32 m. Square with P = 32 has 4 equal sides, so each side = 32 / 4 = 8 meters

FAST Practice Quiz Answers

1

B) 28 cm

P = 2(9) + 2(5) = 18 + 10 = 28 cm. Note: A is just l+w, C and D show area.

2

D) 96 sq m

A = 12 x 8 = 96. Must be square meters because area measures space. C has wrong units.

3

B) 44 ft

P = 2(15) + 2(7) = 30 + 14 = 44 ft. A is just l+w, C and D show area.

4

Select: 8x4, 10x2, and 6x6

8 x 4: P = 2(8)+2(4) = 24
10 x 2: P = 2(10)+2(2) = 24
7 x 5: P = 2(7)+2(5) = 24? NO, = 24. Wait - this IS 24!
6 x 6: P = 2(6)+2(6) = 24
9 x 3: P = 2(9)+2(3) = 24
Correction: ALL five options equal 24! Accept: 8x4, 10x2, 7x5, 6x6, 9x3

5

B) 70 feet

Fence = perimeter. P = 2(20) + 2(15) = 40 + 30 = 70 ft. A is l+w, C and D show area.

6

A) 6 meters

30 = 2(9) + 2w; 30 = 18 + 2w; 12 = 2w; w = 6 m

7

C) 24 sq ft

Covering = area. A = 6 x 4 = 24. Must be square feet. B and D have wrong units.

8

9 (inches)

A = l x w, so 54 = l x 6. l = 54 / 6 = 9 inches

9

D) To find area of a rectangle, multiply length times width.

A) Wrong - perimeter uses regular units, not square units
B) Wrong - area is the space inside, not distance around
C) Wrong - to find perimeter, add (or use P = 2l + 2w)
D) Correct - A = l x w

10

A) 10 ft by 12 ft

A) 10 x 12 = 120 sq ft Correct!
B) 20 x 10 = 200 sq ft X
C) 60 x 60 = 3,600 sq ft X
D) 30 x 30 = 900 sq ft X

FAST Quiz Scoring Guide

Score	Interpretation	Recommended Action
9-10/10	Mastery	Ready for IXL practice on composite figures and more complex perimeter/area problems.
7-8/10	Approaching Mastery	Review missed concepts. Common issues: confusing perimeter/area, wrong units.
4-6/10	Developing	Reteach with manipulatives (grid paper, tiles). Focus on visual models and when to add vs. multiply.
0-3/10	Needs Intervention	Small group instruction. Use hands-on activities (measure real objects). Build conceptual understanding before formulas.

Common Errors to Watch For:

Perimeter/Area confusion: Student multiplies for perimeter or adds for area
Unit errors: Writing "square feet" for perimeter or just "feet" for area
Half-perimeter: Student only adds length + width once (forgets opposite sides)
Computation errors: Correct method but arithmetic mistakes