Find the perimeter and area of the quadrilateral ABCD in which AB= 17 cm , `AD= 9 cm, CD=12 cm angle AVB=90^(@)` and AC=15 cm.

Explanation

Let ABCD be the given quadrilateral in which AB = 9 cm, BC = 40 cm, DA = 15 cm and `angle ABC = 90^(@)`.
In right `Delta`ABC, by Pythagoras' theorem, we have
`AC^(2) = AB^(2) + BC^(2) = (81+1600)cm^(2)`
`= 1681 cm^(2)`
`rArr" "AC = sqrt(1681) cm = 41 cm`.
Area of `Delta ABC=(1)/(2) xx AB xx BC`
`=((1)/(2)xx 9 xx 40) cm^(2) = 180 cm^(2)`.
In `Delta`ACD, let a = AC = 41 cm, b = CD = 28 cm and c = AD = 15 cm.
`therefore" "s=(1)/(2)(41 + 28 + 15)cm=((1)/(2)xx84)cm = 42 cm`.
`therefore" "(s-a)=(42-41)=1cm, (s-b)=(42-28)cm = 14cm and (s-c)=(42-15)cm = 27 cm`.
`therefore" ""area"(Delta ACD)=sqrt(s(s-a)(s-b)(s-c))`
`=sqrt(42 xx 1 xx 14 xx 27)cm^(2)`
`=(14 xx 3 xx 3)cm^(2)=126 cm^(2)`.
`therefore" "` area of quad. ABCD = area(`Delta`ABC) + area(`Delta`ACD)
`=(180 + 126)cm^(2) = 306 cm^(2)`.