In-a-quadrilateral-ABCD-B-is-a-right-angle-diagonal-AC-is-perpendicular-to-CD-BC-21cm-CD-14cm-and-AD-31cm-Find-the-area-of-ABCD-

Question Number 111277 by Aina Samuel Temidayo last updated on 03/Sep/20

In a quadrilateral ABCD, ∠ B is a

right angle, diagonal AC is

perpendicular to

CD, BC = 21 cm, CD = 14 cm and

AD = 31 cm . Find the area of ABCD .

Answered by 1549442205PVT last updated on 03/Sep/20

Commented by 1549442205PVT last updated on 03/Sep/20

Apply {Pythagor}^{'} s theorem for the

triangles ACD and ABC we have

AC = \sqrt{{AD}^{2} - {CD}^{2}} = \sqrt{31^{2} - 14^{2}} = 3 \sqrt{85} (cm)

AB = \sqrt{{AC}^{2} - {BC}^{2}} = \sqrt{765 - 441} = 18 (cm)

The are of the quadrilateral is

S = S_{ABC} + S_{ACD} = \frac{21.18}{2} + \frac{14.3 \sqrt{85}}{2}

= 189 + 21 \sqrt{85} ({cm}^{2})

Commented by Aina Samuel Temidayo last updated on 03/Sep/20

Thanks .