Question

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

Explanation:

Step1: Find base triangle area

The base is a triangle with base $5.3\ \text{cm}$ and height $1.1\ \text{cm}$.
Area of base: $\frac{1}{2} \times 5.3 \times 1.1 = 2.915\ \text{cm}^2$

Step2: Calculate lateral surface area

Sum areas of 3 rectangular faces:
$\text{Area}_1 = 5.3 \times 3.1 = 16.43\ \text{cm}^2$
$\text{Area}_2 = 5.3 \times 2 = 10.6\ \text{cm}^2$
$\text{Area}_3 = 5.3 \times 5.1 = 27.03\ \text{cm}^2$
Total lateral area: $16.43 + 10.6 + 27.03 = 54.06\ \text{cm}^2$

Step3: Calculate total surface area

Add 2×base area to lateral area:
$\text{Total Area} = 54.06 + 2 \times 2.915 = 54.06 + 5.83 = 59.89\ \text{cm}^2$

Step4: Calculate prism volume

Multiply base area by length of prism ($5.3\ \text{cm}$):
$\text{Volume} = 2.915 \times 5.3 = 15.4495\ \text{cm}^3$

Answer:

Total surface area: $59.89\ \text{cm}^2$
Volume: $15.45\ \text{cm}^3$ (rounded to 2 decimal places)