Question

Ask.

Find the area of quadrilateral ABCD. (Hint: the diagonal divides the quadrilateral into two triangles.]
А
7.84
4.57
3.42
horas
D
4.39
С
A. 14.89 units
B. 11.09 units
C. 17.46 units
D. 18.22 units?

Answer 1

`A) 14.89~ units`

Explanation:

`AD=C=3.42~, AC=d=4.57, ~CD=a=4.39`

`S=(C+d+a)/(2) =(3.42+4.57+4.39)/(2) =6.19`

`Using ~ heron's~ formula:`

`Area~ of ADC~is:`

⇒
`√(s(s-c)(s-d)(s-a))`

⇒
`√(6.19(6.19-3.42)(6.19-4.57)(6.19-4.39))`

⇒
`√(6.19*2.77*1.62*1.8)`

⇒
`√(49.9986)` ⇒
`7.071`

`Area ~of ~ ABD ~is:`

⇒
`√(s(s-d)(s-b)(s-a))`

⇒
`√(8.35(8.35-7.84)(8.35-3.42)(8.35-5.44))`

⇒
`√(8.35*0.51*4.93*2.91)`

⇒
`√(61.0937)` ⇒
`7.816`

`So, Area ~ of ~quadrilateral~ ABCD ~ =`

`A=Area ~of ~ADC+Area ~ of ABD:`

`A=7.071+7.816`

`A=14.89 ~units^2`

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