Find the area of the quadrilateral ABCD shown in figure (ii) given below. All measurements are in centimeters.

In right angle △ABD,

⇒ BD² = AB² + AD²

⇒ BD² = 6² + 8²

⇒ BD² = 36 + 64

⇒ BD² = 100

⇒ BD = $\sqrt{100}$ = 10 cm.

In right angle △BDC,

⇒ BC² = BD² + DC²

⇒ 26² = 10² + DC²

⇒ DC² = 676 - 100

⇒ DC² = 576

⇒ DC = $\sqrt{576}$ = 24 cm.

Area of △ABD = $\dfrac{1}{2}$ × base × height

= $\dfrac{1}{2}$ × AD × AB

= $\dfrac{1}{2}$ × 8 × 6

= 24 cm².

Area of △BDC = $\dfrac{1}{2}$ × base × height

= $\dfrac{1}{2}$ × DC × BD

= $\dfrac{1}{2}$ × 24 × 10

= 120 cm².

Area of quadrilateral ABCD = Area of △ABD + Area of △BDC

= 24 + 120 = 144 cm².

Hence, area of quadrilateral ABCD = 144 cm².