4th Grade Area and Perimeter of Rectangles Test Solutions and Scoring (PDF)

4th Grade math test solutions: Area and Perimeter of Rectangles – Maths PDF

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

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

Area perimeter test answers: worked solutions

Question 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.

Question 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.

Question 3 – Find the length [2 pts]

$63 \div 7 = 9$. The length is 9 ft.

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

Question 4 – Find the width [2 pts]

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

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

Question 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 – 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.

Question 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.

Question 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 area perimeter test 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.
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.

How to use this area perimeter test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 4 chapters: Grade 4 math.

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