Question

module 4 :

1. calcule l’aire totale et le volume du prisme à base octogonale suivant

18,87 cm
3 cm
3,62 cm

Explanation:

Step1: Calculate base area

An octagon can be split into 8 congruent isosceles triangles. Area of 1 triangle: $\frac{1}{2} \times 3 \times 3.62 = 5.43$ $\text{cm}^2$. Total base area: $8 \times 5.43 = 43.44$ $\text{cm}^2$.

Step2: Calculate lateral surface area

Perimeter of octagon: $8 \times 3 = 24$ $\text{cm}$. Lateral area: $24 \times 18.87 = 452.88$ $\text{cm}^2$.

Step3: Calculate total surface area

Total area = 2×base area + lateral area: $2 \times 43.44 + 452.88 = 86.88 + 452.88 = 539.76$ $\text{cm}^2$.

Step4: Calculate volume

Volume = base area × height: $43.44 \times 18.87 = 819.7128$ $\text{cm}^3$.

Answer:

Total surface area: $\boldsymbol{539.76\ \text{cm}^2}$
Volume: $\boldsymbol{819.71\ \text{cm}^3}$ (rounded to 2 decimal places)