Question

a net for a three - dimensional figure is shown on grid paper. each square of the grid paper represents 1 in.². what is the surface area of the three - dimensional figure? area of rectangle a = l·w s.a. = 2(6·2)+2(6·3)+2(2·3) s.a. = 28 in.²

Explanation:

Step1: Calculate area of first - type rectangles

The formula for the area of a rectangle is $A = l\times w$. There are two rectangles with dimensions $6\times2$. Their combined area is $2\times(6\times2)=24$ square inches.

Step2: Calculate area of second - type rectangles

There are two rectangles with dimensions $6\times3$. Their combined area is $2\times(6\times3) = 36$ square inches.

Step3: Calculate area of third - type rectangles

There are two rectangles with dimensions $2\times3$. Their combined area is $2\times(2\times3)=12$ square inches.

Step4: Calculate total surface area

The surface area $S.A.$ of the three - dimensional figure is the sum of the areas of all the rectangles in the net. $S.A.=2\times(6\times2)+2\times(6\times3)+2\times(2\times3)=24 + 36+12=72$ square inches.

Answer:

$72$ in.$^{2}$