4th Grade Area and Perimeter of Rectangles Worksheet Answer Key (PDF)

4th grade area and perimeter worksheet answers – Maths PDF

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This 4th grade area and perimeter worksheet answers covers area and perimeter of rectangles (Common Core 4.MD.A.3), with a free PDF to print.

Key takeaway: This answer key helps fourth grade students and parents check area and perimeter work and understand each step.

Topic: Area and Perimeter of Rectangles (4th grade)
Content: Step-by-step answers to 20 worksheet problems
Standards: 4.MD.A.3
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

This answer key helps fourth grade students and parents check area and perimeter work and understand each step. Also, every solution shows the formula used, the numbers substituted, and the final answer with the correct units, either plain units for perimeter or square units for area.

The key covers all 20 problems, including the table in problem 9, the list of rectangles in problem 13, and the multi step word problems. Then, each missing side answer includes a quick check by multiplying or adding back. Also, plan about 15 minutes to compare answers, and redo any problem where your units or formula were different.

Each solution shows the formula, the numbers put in, and the final answer in bold with the correct unit. Remember that area uses square units and perimeter uses plain units. Use the diagrams to check that your answer makes sense.

Grade 4 · Common Core State Standards: 4.MD.A.3

4th grade area and perimeter worksheet answers: worksheet problems 1 to 10

1 – Count the squares

There are 3 rows with 5 squares each: $3 \times 5 = 15$.

15 square units

2 – Area of a rectangle

$A = l \times w = 7 \times 3 = 21$.

21 sq in

3 – Perimeter by adding

$6 + 2 + 6 + 2 = 16$.

16 ft

4 – Perimeter formula

$P = 2 \times 9 + 2 \times 4 = 18 + 8 = 26$.

26 yd

5 – Area of a square

A square is a rectangle with equal sides: $6 \times 6 = 36$.

36 sq in

6 – Perimeter of a square

$4 \times 8 = 32$.

32 ft

7 – Find the area

$12 \times 5 = 60$.

60 sq ft

8 – Find the perimeter

$2 \times 12 + 2 \times 5 = 24 + 10 = 34$.

34 ft

9 – Complete the table

$10 \times 4 = 40$; $2 \times 10 + 2 \times 4 = 28$
$9 \times 6 = 54$; $2 \times 9 + 2 \times 6 = 30$
$11 \times 2 = 22$; $2 \times 11 + 2 \times 2 = 26$

40 sq in and 28 in; 54 sq in and 30 in; 22 sq in and 26 in

10 – Missing width

Divide the area by the length: $48 \div 8 = 6$. Check: $8 \times 6 = 48$.

Width is 6 ft.

6 ft

Worksheet problems 11 and up

11 – Missing length

$72 \div 9 = 8$. Check: $8 \times 9 = 72$.

8 in

12 – Missing side from perimeter

Two lengths: $2 \times 9 = 18$.

Left for two widths: $30 – 18 = 12$.

One width: $12 \div 2 = 6$.

6 in

13 – Same area, many shapes

Pairs with product 18: 1 by 18, 2 by 9, 3 by 6.

$2 \times 1 + 2 \times 18 = 38$
$2 \times 2 + 2 \times 9 = 22$
$2 \times 3 + 2 \times 6 = 18$

3 by 6 has the smallest perimeter, 18 units

14 – Doubling a rectangle

Original: $5 \times 3 = 15$ sq ft; $2 \times 5 + 2 \times 3 = 16$ ft.

Doubled: 10 ft by 6 ft. Area $10 \times 6 = 60$ sq ft; perimeter $2 \times 10 + 2 \times 6 = 32$ ft.

15 sq ft and 16 ft; 60 sq ft and 32 ft

15 – Garden fence

Perimeter: $2 \times 14 + 2 \times 9 = 28 + 18 = 46$ ft.

Cost: $46 \times 3 = 138$ dollars.

Walk around: 14 + 9 + 14 + 9 = 46.

46 ft of fence; $138

16 – Bedroom carpet

Area: $12 \times 10 = 120$ sq ft.

Cost: $120 \times 2 = 240$ dollars.

$240

17 – Fence for a garden plot

Width: $96 \div 12 = 8$ ft.

Perimeter: $2 \times 12 + 2 \times 8 = 24 + 16 = 40$ ft.

40 ft

Worksheet problem 18 and after

18 – Poster board

Ribbon is around the edge: $2 \times 28 + 2 \times 22 = 56 + 44 = 100$ in.

Paper covers the front: $28 \times 22 = 616$ sq in.

100 in of ribbon; 616 sq in of paper

19 – Patio tiles

Area: $15 \times 8 = 120$ tiles.

Boxes: $120 \div 20 = 6$.

6 boxes

20 – Dog pen

Two lengths: $2 \times 10 = 20$.

Two widths: $36 – 20 = 16$, so one width is $16 \div 2 = 8$ ft.

Area: $10 \times 8 = 80$ sq ft.

10 + 8 + 10 + 8 = 36.

Width 8 ft; area 80 sq ft

Key facts behind this 4th grade area and perimeter worksheet answers

Key facts

Area of a rectangle = length × width, measured in square units.
Perimeter of a rectangle = 2 × length + 2 × width, measured in plain units.
A square is a rectangle whose four sides are equal.
Then, if you know the area and one side, divide to find the other side.
Area tells how much to cover; perimeter tells how far around.

Common mistakes with this 4th grade area and perimeter worksheet answers

Students match the number but ignore the units. An area of 21 and an area of 21 square feet are not the same answer, so compare the labels as well.
Students copy the key for problem 13 and miss the reasoning. Also, notice that the rectangle closest to a square has the smallest perimeter.
Students skip the check lines in problems 10 and 11. Instead, multiplying the answer by the known side should give back the area.
Students compare problem 20 only by the width. The question also asks for the area, so check both numbers.

How to use these solutions

Circle your units in the key and in your own work. Finally, most lost points on this topic come from a missing or wrong unit.
Redo each missed problem by drawing a quick rectangle with all four sides labeled. Also, the picture often shows what was missed.
Parents can ask the child to explain why a perimeter is measured in feet but an area is measured in square feet.

Download the 4th grade area and perimeter worksheet answers as a PDF with the button below and keep it with your notes.

4th grade area and perimeter worksheet answers: frequently asked questions

Why does the answer key give both feet and square feet?

Perimeter measures a length, so it is in feet. Area measures how many unit squares fit inside, so it is in square feet. In problem 15, the fence length is in feet, but the cost is in dollars. Always match the unit to what is being measured.

Which rectangle in problem 13 has the smallest perimeter?

The 6 by 3 rectangle has the smallest perimeter among the whole number pairs with an area of 18. Its perimeter is 18 units. The long 18 by 1 rectangle has a perimeter of 38 units, which is the largest. Squares and near squares use the least edge.

How can I check a missing side answer?

Put your answer back into the formula. For problem 11, the length is 8 because 72 divided by 9 is 8, and 8 times 9 gives back 72. For a perimeter problem, add all four sides and compare with the given perimeter.

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