In a rectangle, one side is 80 and the diagonal is 82. Find the area of the rectangle.

A rectangle is a quadrangle in which all angles are right and equal to each other.

In order to calculate the area of ​​a rectangle, you need to multiply its length by its width:

S = a ∙ b;

S = AB ∙ BC;

BC = 80 cm.

In order to find the length of the BC side, consider the triangle ΔABS. This triangle is rectangular. To calculate, we use the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AC ^ 2 = AB ^ 2 + BC ^ 2;

AB ^ 2 = AC ^ 2 – BC ^ 2;

AB ^ 2 = 82 ^ 2 – 80 ^ 2 = 6724 – 6400 = 324;

AB = √324 = 18 cm.

S = 80 18 = 1440 cm2.

Answer: the area of ​​the rectangle is 1440 cm2.