Question

1. calculez la hauteur (h_b) (linéaire) en pi de la forme qui suit : __________ pi
2. calculez lhypoténuse (h_a) (linéaire) en pi de la forme qui suit : __________ pi
3. calculez la surface (△a + b) en pi² de la forme qui suit : __________ pi²
4. calculez le volume en pi³ de la forme présentée : __________ pi³

Explanation:

First, we convert all units to feet (1 foot = 12 inches, so inches are divided by 12 to get feet):

• 8" = $\frac{8}{12} = \frac{2}{3}$ ft
• 10" = $\frac{10}{12} = \frac{5}{6}$ ft
• 24" = $\frac{24}{12} = 2$ ft

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Problem 7: Find $H_B$

Step1: Use Pythagorean theorem

For right triangle B: $H_B = \sqrt{h_B^2 - B_B^2}$
$h_B = 5$ ft, $B_B = 3$ ft
$H_B = \sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4$ ft

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Problem 8: Find $h_A$

Step1: Use $H_A = H_B = 4$ ft

Triangles A and B share the same height $H_A = H_B = 4$ ft

Step2: Apply Pythagorean theorem

$h_A = \sqrt{H_A^2 + B_A^2}$
$B_A = 5$ ft, $H_A = 4$ ft
$h_A = \sqrt{4^2 + 5^2} = \sqrt{16 + 25} = \sqrt{41} \approx 6.403$ ft

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Problem 9: Find total area $\triangle A + \triangle B$

Step1: Area of triangle A

$Area_A = \frac{1}{2} \times B_A \times H_A = \frac{1}{2} \times 5 \times 4 = 10$ ft²

Step2: Area of triangle B

$Area_B = \frac{1}{2} \times B_B \times H_B = \frac{1}{2} \times 3 \times 4 = 6$ ft²

Step3: Sum the two areas

$Total Area = 10 + 6 = 16$ ft²

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Problem 10: Find total volume (A + B)

Step1: Volume of block A

$Volume_A = length \times width \times height = 46 \times 2 \times \frac{5}{6} = \frac{460}{6} \approx 76.667$ ft³

Step2: Volume of block B

$Volume_B = length \times width \times height = 46 \times \frac{2}{3} \times 8 = \frac{736}{3} \approx 245.333$ ft³

Step3: Sum the two volumes

$Total Volume = \frac{460}{6} + \frac{736}{3} = \frac{460 + 1472}{6} = \frac{1932}{6} = 322$ ft³

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Answer:

1. $4$
2. $\sqrt{41} \approx 6.403$
3. $16$
4. $322$