Each side of a square is increasing at a rate of 4 cm/s. at what rate is the area of the square increasing when the area of the square is 25 square centimeters?

The question is related to application of derivatives .

Let A represents the area and s represent the side length .

Differentiating both sides with respect to t

It is given that ds/dt = 4cm/s

Substituting the values of s, ds/dt and on multiplying them, we will get

dA/dt = 2(5)(4) = 40 cm^2/s

Therefore rate of change of area when area= and rate of change of side is 4 cm/s is 40

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2