Question

In quadrilateral ABCD, AB ==DC and AD is perpendicular to AB. Also AB = 8 m, DC =BC = 5 cm. Find the area of the quadrilateral

Answer 1

see diagram.

Area of  ADB : 1/2 * 5 * 8 = 20 cm²

BD² =  AD² + AB² = 25 + 64 = 89
 BD = √89 = 9.43 cm

In the triangle  BDC:
    s = semiperimeter = (9.43 + 5 + 5)/2 = 9.717 cm
   Area = √[ s (s-a)(s-b)(s-c) ] = 7.82 cm²

Area of quadrilateral = 20 + 7.82 = 27.82 cm²