4th Grade Area and Perimeter of Rectangles Test Answer Key and Scoring Guide (PDF)

4th grade area and perimeter test answer key – Maths PDF

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This 4th grade area and perimeter test answer key 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 see how each point on the area and perimeter test was earned.

Topic: Area and Perimeter of Rectangles (4th grade)
Content: Worked solutions and a scoring guide for 8 questions
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 see how each point on the area and perimeter test was earned. Also, it gives a full solution to all eight questions, including the table in question 5 and the three part word problems in questions 6, 7, and 8.

Each solution lists the formula, the substitution, and the answer with units. Then, missing side questions include a check. Add your points out of 20 and then spend about 15 minutes redoing each question that lost credit. Also, if you lost points on units, circle the unit in each solution and notice how it changes between area and perimeter.

Use this answer key to score the test out of 20 points. Each worked solution is followed by a scoring note that explains how many points to give, including partial credit for correct steps and for correct units.

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

4th grade area and perimeter test answer key: worked solutions

1 – Rectangle measures [2 pts]

$11 \times 4 = 44\text{ sq in}$
$2 \times 11 + 2 \times 4 = 22 + 8 = 30\text{ in}$

Scoring: 1 point for each correct answer. Take off the point if the unit is missing or area is given in plain units.

2 – Square measures [2 pts]

$7 \times 7 = 49\text{ sq m}$
$4 \times 7 = 28\text{ m}$

Scoring: 1 point for each correct answer with its unit.

3 – Find the length [2 pts]

$63 \div 7 = 9$. So, the length is 9 ft.

Scoring: 1 point for dividing the area by the width, 1 point for the correct length with its unit.

4 – Find the width [2 pts]

$2 \times 11 = 22$, and $38 – 22 = 16$. Then $16 \div 2 = 8$. So, the width is 8 in.

Scoring: 1 point for finding the total of the two widths (16), 1 point for the correct width.

5 – Missing measures table [3 pts]

A: (a) $8 \times 5 = 40$ sq ft; (b) $2 \times 8 + 2 \times 5 = 26$ ft.

B: (c) $54 \div 9 = 6$ ft.

C: $24 – 2 \times 4 = 16$, and $16 \div 2 = 8$, so (d) is 8 ft.

(a) 40 sq ft; (b) 26 ft; (c) 6 ft; (d) 8 ft

Scoring: 1 point for row A (both values correct), 1 point for row B, 1 point for row C.

Question 6 and after

6 – Backyard fence [3 pts]

$2 \times 25 + 2 \times 18 = 50 + 36 = 86\text{ ft}$
$86 \times 4 = 344$ dollars: $344

25 + 18 + 25 + 18 = 86.

Scoring: part a, 1 point. Part b, 1 point for multiplying the perimeter by 4 and 1 point for the correct cost.

7 – Rug on the floor [3 pts]

$12 \times 10 = 120\text{ sq ft}$
$9 \times 6 = 54\text{ sq ft}$
$120 – 54 = 66\text{ sq ft}$

Room area split.

Scoring: 1 point for each correct area or difference, with square units.

8 – Same perimeter [3 pts]

A: $2 \times 7 + 2 \times 3 = 20$ ft. B: $4 \times 5 = 20$ ft.
A: $7 \times 3 = 21$ sq ft. B: $5 \times 5 = 25$ sq ft.
B is greater by $25 – 21 = 4$ sq ft.

Scoring: 1 point for both perimeters, 1 point for both areas, 1 point for naming B and the difference of 4 sq ft.

Total score

Total

20 points

Key facts behind this 4th grade area and perimeter test answer key

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 test answer key

Students give a correct number with the wrong unit and lose a point. Also, compare the unit in the key, such as sq ft versus ft, with your own.
Students assume that question 8 has a trick. The two rectangles really do have the same perimeter, but the areas differ, which is the point of the question.
Students skip the table check in question 5. Multiply length by width in each row, then verify the perimeter column from the sides.
Students forget part credit in question 7. Each part of a three part question is worth points, so write an answer for every part.

How to learn from your test

Sort lost points into formula errors, arithmetic errors, and unit errors. Fix the largest group first. Repeat this habit on every problem for the best results.
Redo question 6 with a new cost per foot. Then, changing one number shows whether you understand the steps, not just the answer.
Teachers can have students explain question 8 to a partner, since it shows that shapes with equal perimeters can have different areas.

Download the 4th grade area and perimeter test answer key as a PDF with the button below and keep it with your notes.

4th grade area and perimeter test answer key: frequently asked questions

Why can rectangles with the same perimeter have different areas?

Perimeter only adds the sides, but area multiplies them. So, a 7 by 3 rectangle and a 5 by 5 square both have a perimeter of 20. The first has an area of 21 and the second has an area of 25. The more square-like shape covers more.

How do I find the area of the room not covered by a rug?

Find the area of the room, then the area of the rug, and subtract. A 12 by 10 room has an area of 120 square feet, and a 9 by 6 rug covers 54 square feet. The uncovered floor is 120 minus 54, which is 66 square feet.

What if I used the right formula but made an arithmetic error?

You will usually earn partial credit when the formula and setup are correct. Mark the slip, redo that calculation, and write down the correct facts. Common slips are multiplication facts and forgetting to double a sum in perimeter problems.

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