The rectangle

The area of the rectangle is: $$A=a \cdot b$$

Its perimeter is: $$P=a+a+b+b=2a+2b=2(a+b)$$

And, applying the Pythagorean theorem, its diagonal is: $$d=\sqrt{a^2+b^2}$$

Calculate the diagonal and the area of a rectangle of $5 \ cm \times 10 \ cm$.

• Diagonal $$ d^2=(5 \ cm)^2+(10 \ cm )^2 \\ d = \sqrt{25+100} \ cm \\ d= 5\sqrt{5} \ cm $$

• Area $$A= 5 \ cm \cdot 10 \ cm = 50 \ cm^2$$

And so, the area of the rectangle is: $50 \ cm^2$.