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Area of Any Polygon - by Heron's Formula

The area of q...

Question

The area of quadrilateral ABCD given below is 269.2 sq.units
If true then enter $1$ and if false then enter $0$

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Solution

$G i v e n t h a t i n t h e q u a d r i l a t e r a l A B C D A D = D C = A C = a = 20 u n i t s . ∴ Δ A C D i s a n e q u i l a t e r a l t r i a n g l e . S o i t s a r e a = \frac{\sqrt{3}}{4} a^{2} = \frac{\sqrt{3}}{4} 20^{2} {u n i t}^{2} = 173.2 {u n i t}^{2} . A g a i n i n Δ A B C t h e ∠ B = 90^{o} & A B ⊥ A C . S o Δ A B C i s a r i g h t o n e w i t h h y p o t e n u s e A C = 20 u n i t s, B C = 12 u n i t s & A B = x u n i t s . A p p l y i n g P y t h a g o r a s t h e o r e m, w e g e t, A B = x = \sqrt{{A C}^{2} - {B C}^{2}} = \sqrt{20^{2} - 12^{2}} u n i t s = 16 u n i t s . ∴ a r Δ A B C = \frac{1}{2} \times A B \times B C = \frac{1}{2} \times 16 \times 12 {u n i t}^{2} = 96 {u n i t}^{2} . S o a r . q u a d r i l a t e r a l A B C D = a r Δ A C D + a r Δ A B C = (173.2 + 96) {u n i t}^{2} = {269.2 u n i t}^{2} . A n s - a r q u a d r i l a t e r a l A B C D = {269.2 u n i t}^{2} .$

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