Question

find the surface area of the prism using the net. what is the area of the side rectangles? front and back triangles: 64 cm² side rectangles:? cm² bottom rectangle:? cm² surface area:? cm²

Explanation:

Step1: Calculate area of one side - rectangle

The side - rectangles have dimensions 8 cm and 9 cm. The area of a rectangle is $A = l\times w$. For a side - rectangle with length $l = 9$ cm and width $w = 8$ cm, the area of one side - rectangle is $A_1=9\times8 = 72$ $cm^2$.

Step2: Calculate total area of side - rectangles

There are 2 side - rectangles. So the total area of the side - rectangles $A_{sides}=2\times72 = 144$ $cm^2$.

Step3: Calculate area of bottom rectangle

The bottom rectangle has dimensions 4 cm and 9 cm. Using the formula $A = l\times w$, the area of the bottom rectangle $A_{bottom}=4\times9 = 36$ $cm^2$.

Step4: Calculate surface area of the prism

The surface area $SA$ of the prism is the sum of the area of the front and back triangles ($64$ $cm^2$), the area of the side - rectangles ($144$ $cm^2$), and the area of the bottom rectangle ($36$ $cm^2$). So $SA=64 + 144+36=244$ $cm^2$.

Answer:

Side rectangles: $144$ $cm^2$
Bottom rectangle: $36$ $cm^2$
Surface Area: $244$ $cm^2$