Question

1 cm 4 cm 6 cm find the surface area of the prism using the net. what is the total surface area? front and back: 8 cm² rectangles; side: 12 cm² rectangles; top and bottom: 48 cm² rectangles. surface area: ? cm² 1 cm

Explanation:

Step1: Identify areas of each part

We have three types of rectangular areas: front/back, side, top/bottom with areas \(8\space cm^2\), \(12\space cm^2\), and \(48\space cm^2\) respectively. But wait, actually, for a rectangular prism, the surface area is the sum of the areas of all faces. Wait, maybe the given values are per pair? Wait, the problem says front and back (2 faces) have total \(8\), side (2 faces) total \(12\), top and bottom (2 faces) total \(48\)? Wait no, maybe I misread. Wait, let's re - check. Wait, the net of a rectangular prism has 6 faces: 2 of each (length×width, length×height, width×height). Wait, the given values: front and back (let's say length×height) total \(8\), side (width×height) total \(12\), top and bottom (length×width) total \(48\)? Wait, no, actually, to find the total surface area, we need to sum up all the areas of the faces. Wait, the problem gives front and back area as \(8\), side rectangles area as \(12\), top and bottom as \(48\)? Wait, no, maybe the front and back are two faces, side are two faces, top and bottom are two faces. So total surface area is the sum of front/back, side, and top/bottom areas. Wait, the values given: front and back: \(8\space cm^2\), side rectangles: \(12\space cm^2\), top and bottom: \(48\space cm^2\)? Wait, no, that can't be. Wait, maybe the front and back each have area, side each, top and bottom each. Wait, no, the problem says "Front and back: \(8\space cm^2\) rectangles" – maybe that's the total for front and back (i.e., 2 faces), "Side rectangles: \(12\space cm^2\)" (total for 2 side faces), "Top and bottom: \(48\space cm^2\)" (total for 2 top - bottom faces). Then to find the total surface area, we sum these three totals.

Step2: Sum the areas

The formula for total surface area \(SA\) is \(SA=\text{Area of front/back}+\text{Area of side}+\text{Area of top/bottom}\)

Substitute the given values: \(SA = 8+12 + 48\)

First, \(8 + 12=20\), then \(20+48 = 68\)

Answer:

\(68\)