which diagram is a net for this prism? what is the surface area of the triangular prism? square millimeters

Explanation:

Step1: Identify the faces of the prism

The triangular - prism has two congruent right - angled triangular faces with legs 9 mm and 24 mm, and three rectangular faces with dimensions: 6 mm×9 mm, 6 mm×24 mm, and 6 mm×15 mm.

Step2: Calculate the area of the triangular faces

The area of a right - angled triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. For a triangle with base 9 mm and height 24 mm, $A_{triangle}=\frac{1}{2}\times9\times24 = 108$ square mm. Since there are 2 triangular faces, the total area of the triangular faces is $2\times108 = 216$ square mm.

Step3: Calculate the area of the rectangular faces

For the first rectangular face with dimensions 6 mm×9 mm, $A_1=6\times9 = 54$ square mm. For the second rectangular face with dimensions 6 mm×24 mm, $A_2=6\times24 = 144$ square mm. For the third rectangular face with dimensions 6 mm×15 mm, $A_3=6\times15 = 90$ square mm. The total area of the rectangular faces is $A_{rectangles}=54 + 144+90=288$ square mm.

Step4: Calculate the surface area

The surface area of the triangular prism $A = A_{triangles}+A_{rectangles}=216 + 288=504$ square mm.

Answer:

504