which diagram is a net for this prism? what is the surface area of the rectangular prism?

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a rectangular prism is $SA = 2(lw+lh + wh)$, where $l$ is the length, $w$ is the width, and $h$ is the height. Here, $l = 15$ mm, $w = 4$ mm, and $h = 6$ mm.

Step2: Calculate $lw$

$lw=15\times4 = 60$ mm².

Step3: Calculate $lh$

$lh = 15\times6=90$ mm².

Step4: Calculate $wh$

$wh=4\times6 = 24$ mm².

Step5: Substitute into formula

$SA=2(60 + 90+24)$. First, add the values inside the parentheses: $60 + 90+24=174$ mm². Then, multiply by 2: $SA = 2\times174=348$ mm².

For the net, a net of a rectangular prism should have 6 rectangles that can be folded to form the prism. The correct net will have rectangles with dimensions that match the faces of the prism. The second net is correct as it has rectangles with dimensions 15×4, 15×6, and 4×6 which are the face - dimensions of the given rectangular prism.

Answer:

The correct net is the second one. The surface area of the rectangular prism is 348 mm².