The rectangle

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

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

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

Example

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

Diagonal $d^{2} = (5 c m)^{2} + (10 c m)^{2} d = \sqrt{25 + 100} c m d = 5 \sqrt{5} c m$
Area $A = 5 c m \cdot 10 c m = 50 c m^{2}$

And so, the area of the rectangle is: $50 c m^{2}$ .