Question

find the surface area of the prism using the net. what is the area of the front and back triangles? front and back triangles:? cm² side rectangles: cm² bottom rectangle: cm² surface area: cm² hint: area of a triangle b×h÷2

Explanation:

Step1: Calculate area of front - back triangles

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 4$ cm and $h = 8$ cm. The area of one triangle is $A_1=\frac{1}{2}\times4\times8=16$ $cm^2$. The area of the front and back triangles is $A_{triangles}=2\times16 = 32$ $cm^2$.

Step2: Calculate area of side rectangles

There are two side - rectangles with dimensions $8$ cm by $9$ cm. The area of one side - rectangle is $A_{side1}=8\times9 = 72$ $cm^2$. The total area of the two side - rectangles is $A_{sides}=2\times72=144$ $cm^2$.

Step3: Calculate area of bottom rectangle

The bottom rectangle has dimensions $4$ cm by $9$ cm. The area of the bottom rectangle is $A_{bottom}=4\times9 = 36$ $cm^2$.

Step4: Calculate surface area of the prism

The surface area $A$ of the prism is the sum of the areas of the triangles, side - rectangles, and bottom rectangle. So $A=32 + 144+36=212$ $cm^2$.

Answer:

Front and back triangles: $32$ $cm^2$
Side rectangles: $144$ $cm^2$
Bottom rectangle: $36$ $cm^2$
Surface Area: $212$ $cm^2$