Geometry review

### 1.1. Geometry review

**Lesson 1 page 173: **Observe the picture above, point out

a) The sides are parallel to each other;

b) The sides are perpendicular to each other.

__Solution guide:__

- Observe the figure to find the sides are perpendicular to each other, the sides are parallel to each other.

a) Side AB and side DC are parallel

b) Side AB and side AD are perpendicular to each other.

Side AD and Edge DC are perpendicular to each other.

**Lesson 2 page 173: **Draw a square with sides 3cm long. Calculate the perimeter and area of that square.

__Solution guide:__

- Use a ruler and a millet to draw a 3cm square.
- Perimeter = side x 4
- Area = side x side.

*Solution :*

Draw a square by following these steps:

Draw a line segment DC = 3cm.

Draw a line perpendicular to DC at D and a line perpendicular to DC at C.

On each perpendicular line, take the line segment DA = 3cm; CB = 3cm.

Connect A to B, we get a square ABCD with side 3cm.

The perimeter of square ABCD is:

3 x 4 = 12 (cm)

The area of square ABCD is:

3 x 3 = 9 (m^{2})

**Lesson 3 page 173: **Correct write D, false write S.

a) The perimeter of figure 1 is equal to the circumference of figure 2.

b) The area of figure 1 is equal to the area of figure 2.

c) The area of figure 2 is larger than the area of figure 1.

d) The perimeter of figure 1 is larger than the circumference of figure 2.

__Solution guide:__

Apply the formulas:

- Perimeter of rectangle = (length + width) x 2.
- Area of rectangle = length x width.
- Perimeter of square = side x 4
- Area of square = side x side.

*Solution :*

We have :

The perimeter of figure 1 is : (4 + 3) x 2 = 14 (cm)

The area of figure 1 is: 4 x 3 = 12 (m^{2})

The perimeter of figure 2 is: 3 x 4 = 12 (cm)

Area of figure 2 is: 3 x 3 = 9 (cm2)

So sentences a, b, c are wrong, we write S in the blank box; sentence d) is correct, we write D in the blank.

**Lesson 4 page 173: **To pave a rectangular room, people use square ceramic tiles with a side of 20cm. How many bricks are needed to cover the floor of that classroom, knowing that the classroom floor has a width of 5m, a length of 8m and the mortar circuit is negligible?

__Solution guide:__

- To calculate the area of a rectangular classroom, we multiply the length by the width, then convert the area to a unit of measurement that is square decimeters.
- To calculate the area of a brick, we multiply the side by the side.
- To calculate the number of bricks needed, we take the area of the classroom (with the unit of measure being square decimeters) divided by the area of one brick.

*Solution*

The floor area of the classroom is:

8 x 5 = 40 (m^{2})

40m2 = 400 000cm^{2}

The area of the ceramic tile is:

20 x 20 = 400 (cm^{2})

The number of bricks needed is:

400 000 : 400 = 1000 (tablets)

Answer: 1000 bricks.

### 1.2. Geometry review (continued)

**Lesson 1 page 174: **Look at the picture below, point out

a) Line segment parallel to AB;

b) The line segment is perpendicular to BC;

__Solution guide:__

- Observe the figure to find the lines that are perpendicular to each other, the lines that are parallel to each other.

a) The line segment DE is parallel to AB.

b) The line segment CD is perpendicular to BC.

**Lesson 2 page 174: **

Square ABCD and rectangle MNPQ have the same area. Please choose the correct measure for the length of the rectangle

a) 64cm ; b) 32cm ; c) 16cm ; d) 12cm.

__Solution guide:__

- Area of square = side x side.
- Square ABCD and rectangle MNPQ have the same area, so we have the area of rectangle MNPQ.
- Rectangle length = area : width.

*Solution :*

The area of square ABCD is :

8 x 8 = 64 (cm^{2})

Square ABCD and rectangle MNPQ have the same area, so the area of rectangle MNPQ is 64cm^{2}.

The length of the rectangle MNPQ is:

64 : 4 = 16 (cm)

So the correct answer is c.

**Lesson 3 page 174: **Draw a rectangle 5cm long and 4cm wide. Calculate the perimeter and area of that rectangle.

__Solution guide:__

- Perimeter of rectangle = (length + width) x 2.
- Area of rectangle = length x width.

*Solution :*

Draw a rectangle by following these steps:

- Draw a line segment DC = 5cm.
- Draw a line perpendicular to DC at D, on that line take line segment DA = 4cm.
- Draw a line perpendicular to DC at C. On that line take the line segment CB = 4cm.
- Connecting A and B we get a rectangle ABCD with length 5cm and width 4cm.

The perimeter of rectangle ABCD is:

(5 + 4) x 2 = 18 (cm)

The area of rectangle ABCD is:

5 x 4 = 20 (cm^{2})

**Lesson 4 page 174: **Let H formed by parallelogram ABCD and rectangle BEGC as shown below. Calculate the area of figure H.

__Solution guide:__

- Area of a parallelogram = base length x height.
- Area of rectangle = length x width.
- Area H = area of parallelogram ABCD + area of rectangle BEGC.

*Solution :*

Figure H consists of parallelogram ABCD and rectangle BEGC.

We have BEGC is a rectangle, so BC = GE = 4cm.

The area of parallelogram ABCD is:

4 x 3 = 12 (cm^{2})

The area of rectangle BEGC is:

4 x 3 = 12 (cm^{2})

The area of figure H is:

12 + 12 = 24 (cm^{2})

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