This handy Math in Focus Grade 4 Workbook Answer Key Chapter 12 Practice 3 Rectangles and Squares detailed solutions for the textbook questions.

## Math in Focus Grade 4 Chapter 12 Practice 3 Answer Key Rectangles and Squares

**Find the area of each figure.**

**Example**

Area of the rectangle = 12 × 6

= 72 ft^{2}

The area of the rectangle is 72 square feet.

Question 1.

Area of the square = _________ × __________

= __________ cm^{2}

The area of the square is _____________ square centimeters.

Answer:

Area of the square = **9 cm × 9 cm**

= **81 cm ^{2}**

The area of the square is

**81**square centimeters.

**Solve. Show your work.**

**Example**

The area of a rectangular hall is 78 square yards. Its width is 6 yards. Find the length.

Length × width = area

Length × 6 = 78 yd^{2}

Length = 78 ÷ 6

= 13 yd

The length of the hall is 13 yards.

Question 2.

A rectangle has an area of 56 square centimeters. Its length is 8 centimeters. Find the width.

The width of the rectangle is ___________ centimeters.

Answer:

Length = 8 cm

width = ?

Area of the rectangle = 56 cm^{2}

Area of the rectangle = length × width

56 cm^{2 }= 8 cm x width

56 cm^{2 }÷ 8 cm = width

**7 cm = width **

The width of the rectangle is **7** centimeters.

**Solve. Show your work.**

Question 3.

The area of a rectangular carpet is 84 square meters. Its width is 7 meters.

a. Find the length.

Answer:

Length = ?

width = 7 m

Area of the rectangular carpet = 84 m^{2}

Area of the rectangular carpet = length × width

84 m^{2 }= length x 7 m

84 m^{2 }÷ 7 m = length

**12 m = length**

The length of the rectangular carpet is **12 **meters.

b. Find the perimeter of the carpet.

Answer:

Perimeter of the carpet = 7 m + 12 m + 7 m + 12 m

= 38 m

Perimeter of the carpet is **38** meters.

Question 4.

The area of a square is 64 square inches. Find the length of one side of the square.

(Hint: What number multiplied by itself is equal to 64?)

Answer:

Area = side × side = s^{2
}Where s is the length of the side of the square.

Area of a square is 64 square inches.

64 in^{2}= s^{2
}(8 in)^{2}= s^{2
}**8 inches = s**

The length of one side of the square is 8 inches.

Question 5.

The area of a square garden is 100 square meters.

a. Find the length of each side of the garden.

Answer:

A square is a regular polygon with four sides.

Area = width × height

But since the width and height are by definition the same, the formula is usually written as

Area = side × side = s^{2
}where *s* is the length of one side.

To find the length of each side of the garden we know that the area is 100 applying the area formula and solving for *s, *the length of one side, we get that

100 m^{2}= s^{2}

(10 m)^{2 }= s^{2
}**10 m = s
The length of each side of the garden is 10 m.**

b. Find the perimeter of the garden.

Answer:

In the case of a square, all four sides are the same length, so the perimeter is four times the length of a side.

We find that the length of each side is 10 m. Therefore, the perimeter is

Perimeter = 4 × s

= 4 x 10 m

= 40 m

where *s* is the length of any one side.

**The perimeter of the garden is 40 m.**

**Solve. Show your work.**

Question 6.

The area of a rectangular recreation area is 45 square miles. Its width is 5 miles.

a. Find the length.

Answer:

Length = ?

width = 5 mi

Area of the rectangular recreation = 45 mi^{2}

Area of the rectangular recreation = length × width

45 mi^{2 }= length x 5 mi

45 mi^{2 }÷ 5 mi = length

**9 mi = length**

The length of the rectangular recreation is **9 **miles.

b. Find the perimeter.

Answer:

Perimeter of the rectangular recreation = 9 mi + 5 mi + 9 mi + 5 mi

= 28 miles

Perimeter of the rectangular recreation is **28 miles**.

Question 7.

The perimeter of a rectangular poster is 156 inches. Its width is 36 inches.

a. Find the length.

Answer:

Length = ?

**width = 36 in**

**perimeter of a rectangular poster = 156 in**

Perimeter of the rectangular poster = length + width + length + width

156 in = l + 36 in + l + 36 in

156 in = 2l + 72 in

156 in – 72 in = 2l

84 in = 2l

**42 in = l**

The length of the rectangular poster is** 42 inches**.

b. Find the area.

Answer:

Length = 42 inches

width = 36 inches

Area of the rectangular poster = length x width

= 42 inches x 36 inches

= **1,512 in ^{2 }**

Area of the rectangular poster is 1,512 square inches.