Question

20. In Fig. 10.16, the angle BAD and ADC are right angles
and AX is parallel to BC. If AB = BC = 5 cm, and
DC = 8 cm. Calculate the area of ABCX.
(From Pythagoras theorem) ​

Answer 1

Answer:

Step-by-step explanation:

Given: Angle BAD = Angle ADC = 90

           AB = BC = 5cm

           DC = 8cm

Since XC || AB and AX || BC

ABCX is a parallelogram

=> AB = XC ----(1)

Therefore, DC = XC + DC

DX = DC - XC

     = DC - AB    [From (1)]

     = 8 - 5

     = 4 cm

In Triangle DAX,

By Pythogoras Theorum,

XA^2 = AD^2 + DX^2

DA^2 = XA^2 - DX^2

         =  5^2 - 4^2

         = 25 - 16

Therefore, DA = Square root of 9

                        = 3cm

                        = Height of Parrallelogram

Area of Paralleogram = base x height

                                    = AB x AD

                                    = 5 x 3

                                    = 15 cm^2