Question

a triangular prism is shown below.15 cm17 cm40 cm8 cmwhich diagram is a net for this prism?what is the surface area of the triangular prism?square centimeters

Explanation:

Step1: Identify net of the prism

The triangular prism has two right triangular bases (legs 8 cm, 15 cm, hypotenuse 17 cm) and three rectangular faces with lengths 40 cm, paired with each side of the triangle. The correct net has one rectangle attached to each side of the triangular bases, matching the side lengths: 40 cm × 8 cm, 40 cm × 15 cm, 40 cm × 17 cm, with the two right triangles (8 cm, 15 cm, 17 cm) attached to the matching sides of the rectangles. This corresponds to the right-hand diagram (blue border).

Step2: Calculate area of triangular bases

The triangular base is a right triangle, so area is $\frac{1}{2} \times \text{base} \times \text{height}$.
$\text{Area of 1 triangle} = \frac{1}{2} \times 8 \times 15 = 60$
$\text{Total area of 2 triangles} = 2 \times 60 = 120$

Step3: Calculate area of rectangular faces

Calculate area of each rectangle:

• Rectangle 1: $8 \times 40 = 320$
• Rectangle 2: $15 \times 40 = 600$
• Rectangle 3: $17 \times 40 = 680$

$\text{Total area of rectangles} = 320 + 600 + 680 = 1600$

Step4: Total surface area

Add the area of the triangular bases and rectangular faces.
$\text{Total Surface Area} = 120 + 1600 = 1720$

Answer:

1. The correct net is the right-hand diagram (blue border).
2. 1720 square centimeters