Reviewing the perimeter and area of some shapes

### 1.1. Knowledge to remember

1) Rectangle

P = (a + b) × 2

S = a × b

2) Triangle

\(S = \frac{{a \times h}}{2}\)

3) Square

P = a × 4

S = a × a

4) Trapezoid

\(S = \frac{{(a + b) \times h}}{2}\)

5) Parallelogram

S = a × h

6) Rhombus

\(S = \frac{{m \times n}}{2}\)

7) Round shape

C = r × 2 × 3.14

S = r × r × 3.14

### 1.2. Solve textbook exercises on pages 166, 167

**Lesson 1 Textbook page 166**

A rectangular orchard has a length of 120m and a width equal to 2/3 of its length.

a) Calculate the perimeter of that garden.

b) Calculate the area of that garden in square meters, hectares.

__Solution guide:__

a) The width of the rectangular garden is:

\(120 \times \frac{2}{3} = 80\:(m)\)

The perimeter of the rectangular garden is:

+ 80) × 2 = 400(square meter)

b) The area of the rectangular garden is:

80 = 9600(square meter^{2})

= 0,96Ha

Answer: a) ;

b) ; 96Ha

Lesson 2 Textbook page 167

The figure below is a trapezoidal plot of land drawn on a 1:1000 scale map. Calculate the area of that land in square meters.

__Solution guide:__

The length of the great base of a trapezoid is:

5×1000=5000(cm)

5000cm=50m

The length of the small base of a trapezoid is:

3×1000=3000(cm)

3000cm=30m

The height of the trapezoidal plot is:

2×1000=2000(cm)

2000cm=20m

The area of the trapezoidal plot is:

\(\frac{{(50 + 30) \times 20}}{2} = 800({m^2})\)

Answer: 800m^{2}

Textbook page 167

On the figure below, calculate the area:

a) Square ABCD

b) The colored part of the circle.

__Solution guide:__

a) The area of square ABCD is 4 times the area of triangle BOC. Triangle BOC is a right triangle with the lengths of two sides 4cm and 4cm.

The area of right triangle BOC is:

\(\frac{{4 \times 4}}{2} = 8\:(c{m^2})\)

The area of square ABCD is:

8 × 4 = 32 (cm^{2})

b) The area of the shaded part of the circle is equal to the area of the circle with radius 4cm minus the area of square ABCD

The area of the circle is:

4 × 4 × 3.14 = 50.24(cm^{2})

The area of the shaded part of the circle is:

50.24 − 32 = 18.24(cm^{2})

Answer: a) 32cm^{2}

b) 18.24cm^{2}

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