Question

the sides of a quadrilateral taken in order are 9m ,40m,15m and 28 m respectively .The conbined by the first two sides is a right angle .find its area

Answer 1

let ABCD is a quadrilateral in which AB =9m , BC= 40 m , CD=15m and DA=28m
join , AC
now in triangle ABC ,as angle B =90°
therefore , ar.(∆ABC) =1/2 *9*40
ar. (∆ABC) =180°
Now by Pythagoras theorem
(AC)^2 = (AB)^2+(BC)^2
(AC)^2 = (9)^2+(40)^2
(AC)^2 = 81 + 1600
AC = √1681
AC =41
Now find the area of triangle ADC by heron's formula and add the area of triangle ABC to it
You will get the area of quadrilateral ABCD