Math New Drill : Level 1 SNJ00-1011-L1 Area of quadrangle

There is a quadrangle ABCD as shown in the figure below. 
AB＝AD＝6cm. AC＝8cm. ∠A＝∠C＝90 degrees.
Find the area of quadrangle ABCD.









Answer
32 cm2

Solution
In the Fig.1,  ○ + ● = 90 degrees and ∠X + ∠Y = 360 - 90 × 2 = 180 degrees.

Divide this quadrangle as shown in the Fig.2 and connect as shown in the Fig.3.


This figure becomes a right-angled isosceles triangle. 

Therefore the area of this figure is 8 × 8 / 2 = 32 cm2.