Question

Polygon ABCD is a rectangle what is the area

Answer 1

Solution:

As, You have Written Polygon ABCD is a rectangle.

It is a Four sided Polygon , having all it's interior angles equal to 90°.As well as Opposite sides are equal(AB=CD,AD=BC), equal diagonals(AC=B D).

Join any of the diagonal of Rectangle either AC or B D.

In Right Δ ABC , Right angled at B

${\text{Area (Right triangle ABC)}} =\frac{1}{2}\times AB \times BC$---(1)

In Right  Δ ADC  , Right angled at D      

${\text{Area (Right triangle ABC)}} =\frac{1}{2}\times AD \times DC$---(2)

Adding (1) and (2) that is LHS to LHS and RHS to RHS

Ar( Δ ABC) +Ar( Δ ADC)$=\frac{1}{2}\times[ AB \times BC+ AD \times DC]\\\\=\frac{1}{2}[2 \times AB \times BC][\text{As, AB=CD, and BC=AD}]\\\\ = AB \times BC$

So, Area of Rectangle= Product of any two Adjacent Sides