Area and Perimeter: math practice, Grade 3 – download the PDF

1 Count the squares ★★★

Each square in the figure has sides of 1 cm.

How many unit squares cover the rectangle? Write its area with the correct unit.

2 Floor tiles in a hallway ★★★

Ms. Rivera covers a hallway floor with 1-foot square tiles. She lays 3 rows with 9 tiles in each row.

1. How many tiles does she use?
2. What is the area of the hallway floor?

3 Brownie pan ★★★

A pan holds brownies cut into 1-inch squares: 4 rows with 6 brownies in each row.

1. Write a multiplication sentence for the number of brownies.
2. What is the area of the pan?

4 Areas of rectangles ★★★

Find the area of each rectangle.

1. 6 cm by 3 cm
2. 8 in by 5 in
3. 7 m by 2 m

5 Areas of squares ★★★

Find the area of each square.

1. A square tile with sides of 5 in.
2. A square card with sides of 8 cm.

6 Perimeter of a triangle ★★★

A triangle-shaped flag has sides of 7 in, 9 in, and 6 in. What is its perimeter?

7 A garden bed ★★★

A rectangular garden bed is 9 ft long and 4 ft wide.

1. Find its area.
2. Find its perimeter.

8 The missing side of a rectangle ★★★

A rectangular playground has an area of 56 square meters. Its width is 7 m. What is its length?

9 Cut it into two parts ★★★

A rectangle is 7 units wide and 6 units tall. It is cut into two parts, one 4 units wide and one 3 units wide.

1. Find the area of each part.
2. Add to find the area of the whole rectangle.
3. Check by multiplying \(7 \times 6\).

10 L-shaped patio ★★★

The figure shows a patio. All lengths are in feet. The dashed line cuts it into two rectangles.

Find the area of the patio.

11 Fence around a yard ★★★

Mr. Chen wants to put a fence around a rectangular yard that is 12 ft long and 5 ft wide. How many feet of fence does he need?

12 Perimeter of a pentagon ★★★

A pentagon has sides of 4 cm, 6 cm, 5 cm, 7 cm, and 3 cm. Find its perimeter.

13 The third side ★★★

A triangle has a perimeter of 24 cm. Two of its sides are 9 cm and 7 cm. How long is the third side?

14 Which rug is larger? ★★★

Rug A is 6 ft by 4 ft. Rug B is a square with sides of 5 ft.

1. Find the area of each rug. Which one covers more floor?
2. Find the perimeter of each rug.
3. What do you notice?

15 Same area, different shapes ★★★

A craft store sells rectangular mats with an area of 24 square inches. The side lengths are whole numbers of inches.

1. List every possible length and width pair (do not count a rotated copy twice).
2. Find the perimeter of each mat.
3. Which mat has the smallest perimeter?

16 Same perimeter, different shapes ★★★

Rectangles with whole-number sides all have a perimeter of 20 cm.

1. Find the width of each one if the length is 9, 8, 7, 6, or 5 cm.
2. Find the area of each rectangle.
3. Which one has the greatest area?

17 Width first, then area ★★★

A rectangular pool has a perimeter of 26 m and a length of 8 m. Find its width and then its area.

18 From perimeter to area of a square ★★★

A square picture frame has a perimeter of 36 cm. What is the area of the picture inside, if the picture has the same size as the frame?

19 Carpet in a room ★★★

A bedroom floor is 9 ft by 7 ft. A rectangular carpet that is 5 ft by 4 ft lies on the floor. How many square feet of the floor are not covered by the carpet?

20 A notched shape ★★★

The figure shows a rectangle with a notch cut from its top right corner. All lengths are in centimeters.

1. Find the missing side marked with a question mark.
2. Find the perimeter of the shape.
3. Find its area.

21 A banner and the distributive property ★★★

A school banner is 12 ft long and 7 ft tall. Break 12 into \(10 + 2\) and use the distributive property to find the area.

22 Is Mia right? ★★★

Mia says: “If a rectangle has a longer perimeter, it always has a larger area.” Test her idea with a 1 by 12 rectangle and a 4 by 4 square, both in inches.

1. Find the perimeter and area of each shape.
2. Is Mia right? Explain.