Question

find the surface area of the prism using the net. what is the area of the front and back rectangles? front and back: ? cm² side rectangles: cm² top and bottom: cm² surface area: cm²

Explanation:

Step1: Calculate area of front and back rectangles

The front and back rectangles have dimensions 6 cm (height) and 4 cm (width). The area of a rectangle is $A = l\times w$. So for each of the front - back rectangles, $A_{1}=6\times4 = 24$ $cm^{2}$. The total area of the front and back rectangles is $2\times24=48$ $cm^{2}$.

Step2: Calculate area of side rectangles

The side rectangles have dimensions 6 cm (height) and 1 cm (width). The area of each side rectangle is $A_{2}=6\times1 = 6$ $cm^{2}$. The total area of the two side rectangles is $2\times6 = 12$ $cm^{2}$.

Step3: Calculate area of top and bottom rectangles

The top and bottom rectangles have dimensions 4 cm (length) and 1 cm (width). The area of each top - bottom rectangle is $A_{3}=4\times1=4$ $cm^{2}$. The total area of the top and bottom rectangles is $2\times4 = 8$ $cm^{2}$.

Step4: Calculate surface area

The surface area $SA$ of the prism is the sum of the areas of all the rectangles. $SA=48 + 12+8=68$ $cm^{2}$.

Answer:

Front and back rectangles: 48 $cm^{2}$
Side rectangles: 12 $cm^{2}$
Top and bottom rectangles: 8 $cm^{2}$
Surface Area: 68 $cm^{2}$