Area of rectangles and squares

**Lesson 1:** Find the area and perimeter of a rectangle with length 4 cm and width 8 cm.

**Solution guide:**

- The area of a rectangle is equal to the length times the width (same unit of measure).
- Perimeter of a rectangle is equal to length plus width (same units) and then multiply by two.

*Solution*

Change: 4dm = 40cm

The area of the rectangle is:

40 x 8 = 320 (cm^{2})

Perimeter of the rectangle is:

(40 + 8) x 2 = 96 (cm)

Answer: 320 cm^{2}

96 cm

**Lesson 2:** Figure H consists of rectangle ABCD and rectangle DMNP (with dimensions shown in the figure).

a) Calculate the area of each rectangle in the figure

b) Calculate the area of figure H.

__Solution guide:__

- Calculate the area of two rectangles ABCD and DMNP when the length and width are known.
- The area of shape H is equal to the sum of the areas of the two rectangles just found.

a) The area of rectangle ABCD is :

8 x 10 = 80 (cm^{2})

The area of rectangle DMNP is :

20 x 8 = 160 (cm^{2})

b) The area of figure H is :

80 + 160 = 240 (cm^{2})

Answer: a) 80 cm2; 160 cm2 b) 240cm^{2}

**Lesson 3:** A rectangle has a width of 5cm, length twice its width. Calculate the area of that rectangle.

__Solution guide:__

*Summary:*

Width: 5cm

Length: Twice the width.

Acreage: ? cm^{2}

– Find the length of the rectangle.

– Find the area of the rectangle.

*Solution*

The length of the rectangle is:

5 x 2 = 10 (cm)

The area of the rectangle is:

10 x 5 = 50 (cm^{2})

Answer: 50 cm^{2}

**Lesson 4:** Find the area of a square whose side is

a) 7 cm

b) 5 cm

__Solution guide:__

- The area of a square is equal to the length of one side multiplied by the number itself.

a) The area of the square is:

7 x 7 = 49(cm2)

b) The area of the square is:

5 x 5 = 25 (cm2)

**Lesson 5: **To add a wall, people use all 9 ceramic tiles, each tile is 10cm square. How much gasoline – ti – square meter is the area of the wall paneled?

__Solution guide:__

- Find the area of a square brick by multiplying the length of one side by itself.
- Find the area of the additional wall panel that is equal to the area of one brick multiplied by 9.

*Solution*

The area of a ceramic tile is:

10 x 10 = 100 (cm^{2})

The additional wall area is:

100 x 9 = 900 (cm^{2})

Answer: 900 cm^{2}

**Lesson 6:** Given rectangle ABCD and square EGHI (with dimensions shown in the figure)

a) Calculate the area and perimeter of each figure;

b) Compare the area and perimeter of rectangle ABCD with the area and perimeter of square EGHI.

__Solution guide:__

- Area of a rectangle equal to product of length and width (same unit of measure)
- The perimeter of the rectangle is equal to the length plus the width (in the same units) and then multiplied by two.
- The area of a square is equal to the product of the length of a side times the number itself.
- The perimeter of a square is equal to the product of the length of one side multiplied by 4.
- Compare numbers that contain the same unit of measure: Compare the same as with natural numbers.

a) The area of rectangle ABCD is :

5 x 3 = 15 (cm^{2})

Perimeter of rectangle ABCD is

(5 + 3) x 2 = 16 (cm)

The area of square EIGH is :

4 x 4 = 16(cm^{2})

Perimeter of square EIGH is :

4 x 4 = 16 (cm)

.

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