Question

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

Explanation:

Step1: Calculate area of front - back triangles

The formula for the area of a triangle is $A=\frac{b\times h}{2}$. For the front - back triangles, $b = 4$ cm and $h = 8$ cm. The area of one triangle is $\frac{4\times8}{2}=16$ $cm^{2}$. The area of the front and back triangles together is $2\times16 = 32$ $cm^{2}$.

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 $A = 8\times9=72$ $cm^{2}$, and the total area of the two side rectangles is $2\times72 = 144$ $cm^{2}$.

Step3: Calculate area of bottom rectangle

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

Step4: Calculate surface area of the prism

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

Answer:

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