a triangular prism is shown below. which diagram is a net for this prism? what is the surface area of the…

Explanation:

Step1: Identify the faces of the prism

The triangular prism has 2 triangular faces and 3 rectangular faces. The triangular faces have base - 10 mm and height - 24 mm. The rectangular faces have dimensions: 20×10, 20×26, 20×24.

Step2: Calculate the area of the triangular faces

The area formula for a triangle is $A=\frac{1}{2}bh$. For a triangle with $b = 10$ mm and $h=24$ mm, $A_{triangle}=\frac{1}{2}\times10\times24=120$ square - mm. Since there are 2 triangular faces, the total area of the triangular faces is $2\times120 = 240$ square - mm.

Step3: Calculate the area of the rectangular faces

For the first rectangular face with dimensions 20×10, $A_1=20\times10 = 200$ square - mm. For the second rectangular face with dimensions 20×26, $A_2=20\times26 = 520$ square - mm. For the third rectangular face with dimensions 20×24, $A_3=20\times24 = 480$ square - mm. The total area of the rectangular faces is $A_{rectangles}=200 + 520+480=1200$ square - mm.

Step4: Calculate the surface area

The surface area $A$ of the triangular prism is the sum of the area of the triangular faces and the area of the rectangular faces. So, $A=240 + 1200=1440$ square - mm.

Answer:

1440