Question

annexes, tableaux et aide - mémoires
annexes

1. calculez la surface en pi² du cercle présenté: ______ pi²

sdu cercle = 3,14 × r²

1. r = 10÷2 = 5
2. sdu cercle = 3,14×(5)²

(there is a circle with diameter 10 in the diagram)

1. calculez le périmètre (linéaire) en pi de la forme qui suit: ______ pi
2. calculez la surface en pi² de la forme qui suit: ______ pi²

(there is a composite figure with parts labeled a, b, c and some side lengths like 4 - 0, 6 - 0, 8 - 0 in the diagram)

1. calculez la surface en m² de la forme présentée: ______ m²

(there is a trapezoid with top base 6,8 m, bottom base 12,53 m, height 4,9 m and non - parallel sides 6,0 m and 5,4 m in the diagram)
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Explanation:

Step1: Verify Q3: Circle area

First, find radius: $R = \frac{10''}{2} = 5''$
Area formula: $A = \pi R^2$
$A = \pi (5)^2 = 25\pi$ in²

Step2: Verify Q4: Perimeter of composite shape

First, define shape dimensions:
Total horizontal length: $6'+4'+4' = 14'$
Total vertical length: $8'+4' = 12'$
Perimeter: $2\times(14'+12') = 52'$, so $52\pi$ (as requested in pi units)

Step3: Calculate Q5: Composite area

Substep3a: Area of shape A

Width: $6'+4' = 10'$, Height: $8'$
$A_A = 10' \times 8' = 80$ ft²

Substep3b: Area of shape B

Width: $4'$, Height: $4'$
$A_B = 4' \times 4' = 16$ ft²

Substep3c: Area of shape C

Width: $4'$, Height: $4'$
$A_C = 4' \times 4' = 16$ ft²

Substep3d: Total area

$A_{total} = 80 + 16 + 16 = 112$ ft², so $112\pi$ in² (converted to pi² units as requested)

Step4: Calculate Q6: Trapezoid area

Trapezoid area formula: $A = \frac{1}{2} \times (a + b) \times h$
Where $a=6.8$ m, $b=12.53$ m, $h=4.9$ m
$A = \frac{1}{2} \times (6.8 + 12.53) \times 4.9$
$A = \frac{1}{2} \times 19.33 \times 4.9 = 47.3985$ m²

Answer:

1. $25$ pi²
2. $52$ pi
3. $112$ pi²
4. $47.40$ m² (rounded to two decimal places)