Question

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

Explanation:

Step1: Calculate area of front - back rectangles

The front and back rectangles have dimensions 6 cm (height) and 4 cm (width). The area of a rectangle is $A = lw$. So, $A_{front - back}=6\times4 = 24$ $cm^{2}$ for each rectangle. The total area of 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). Using the rectangle - area formula $A = lw$, we get $A_{side}=6\times1 = 6$ $cm^{2}$ for each side rectangle. The total area of side rectangles is $2\times6 = 12$ $cm^{2}$.

Step3: Calculate area of top - bottom rectangles

The top and bottom rectangles have dimensions 4 cm (length) and 1 cm (width). Using the rectangle - area formula $A = lw$, we get $A_{top - bottom}=4\times1 = 4$ $cm^{2}$ for each top - bottom rectangle. The total area of 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. So, $SA=48 + 12+8=68$ $cm^{2}$.

Answer:

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