Question

15 find the surface area of the right triangular prism shown below. a 33 square units b 40 square units c 54 square units d 60 square units

Explanation:

Step1: Calculate area of 2 triangular bases

The right triangle has legs $\frac{3}{2}$ and 2. Area of one triangle: $\frac{1}{2} \times \frac{3}{2} \times 2 = \frac{3}{2}$. Total for 2 triangles: $2 \times \frac{3}{2} = 3$.

Step2: Calculate area of 3 rectangular faces

• Face 1: $\frac{3}{2} \times 5 = \frac{15}{2}$
• Face 2: $2 \times 5 = 10$
• Face 3: $\frac{5}{2} \times 5 = \frac{25}{2}$

Sum of rectangles: $\frac{15}{2} + 10 + \frac{25}{2} = \frac{15+25}{2} + 10 = 20 + 10 = 30$.

Step3: Total surface area

Add base and rectangle areas: $3 + 30 = 33$.

Answer:

A. 33 square units