Question

module 4 : les prismes et les cylindres

1. l’aire totale de ce prisme à base triangulaire est de 1044 cm².
2. quelle est la mesure de la hauteur (h) de ce prisme?
3. quel est le volume du prisme?

Explanation:

Step1: Calculate base area

The triangular base is a right triangle, so area is $\frac{1}{2} \times 9 \times 12 = 54$ $\text{cm}^2$

Step2: Find lateral surface area

Total area = 2×base area + lateral area. So lateral area = $1044 - 2\times54 = 1044 - 108 = 936$ $\text{cm}^2$

Step3: Calculate perimeter of base

Perimeter of triangular base = $9 + 12 + 15 = 36$ $\text{cm}$

Step4: Solve for height $h$

Lateral area = perimeter × $h$, so $h = \frac{936}{36} = 26$ $\text{cm}$

Step5: Calculate prism volume

Volume = base area × $h$ = $54 \times 26 = 1404$ $\text{cm}^3$

Answer:

1. The measure of the height $h$ is 26 cm
2. The volume of the prism is 1404 $\text{cm}^3$