The length of the rectangular plate was reduced by 20% and the width was increased by 20%. Has the area of the plate changed?

Perform the solution to the problem according to the steps:

1) find the area of the plate (rectangle) as the product of length and width:

S1 = a * b sq. units;

2) find a new length size:

(a – 0.2 * a) = 0.8 units;

3) find the new width dimension:

b * 1.2 units;

4) determine the area of the modified plate:

S2 = a * 0.8 * b * 1.2 = 0.96 * a * b sq. units;

5) find the change in area:

S1 – S2 = a * b – 0.96 * a * b = 0.04 * a * b sq. units;

6) find the area reduction in%:

0.04 * 100% = 4%.

Answer: the area of the plate has decreased by 4%.