find-the-Area-ABCD-

Question Number 198477 by a.lgnaoui last updated on 20/Oct/23

find the Area (ABCD)

Commented by a.lgnaoui last updated on 20/Oct/23

Commented by mr W last updated on 21/Oct/23

A r e a (A B C D) = \frac{x^{2} - y^{2}}{4}

Answered by mr W last updated on 21/Oct/23

Commented by mr W last updated on 21/Oct/23

b^{2} = d^{2} + f^{2} \dots (i)

a^{2} = c^{2} + {(f + c + d)}^{2} = c^{2} + f^{2} + c^{2} + d^{2} + 2 f c + 2 f d + 2 c d \dots (i i)

(i i) - (i) :

a^{2} - b^{2} = 2 c^{2} + 2 f c + 2 f d + 2 c d

\Rightarrow c^{2} + f c + f d + c d = \frac{a^{2} - b^{2}}{2}

[A B C D] = \frac{d f}{2} + \frac{c (f + c + d)}{2}

= \frac{c^{2} + d f + c f + c d}{2} = \frac{a^{2} - b^{2}}{4} ✓

Commented by a.lgnaoui last updated on 21/Oct/23

exactly thanks