what is the area of a sector which has an inside angle of 43 degrees and a length of 7 cm?

I assume, by "length," you mean "arc length"...if so, we need to find the radius , first.......

So we have

s = rΘ   where s is the arc length and Θ is in radians........so converting 43° to radians, we have about .75 rads.

So, the radius is given by

r = (7 cm)/.75 = 9.33cm

And the area is given by:

A = (1/2)r²Θ    where  Θ is in radians..........so we have

A = (1/2)(9.33cm)²(.75) =  about 3.5cm²