Question

Polygon ABCD is a rectangle what is the area

Answer 1

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)}} =(1)/(2)* AB * BC`---(1)

In Right Δ ADC , Right angled at D

`{\text{Area (Right triangle ABC)}} =(1)/(2)* AD * DC`---(2)

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

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

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