In the given figure ABCD is quadrilateral in which ∠ABC = 90°, ∠BDC = 90°, AC = 17 cm, BC = 15 cm, BD = 12 cm and CD = 9 cm. The area of quad ABCD is

Question

In the given figure ABCD is quadrilateral in which ∠ ABC = 90°, ∠ BDC = 90° , AC = 17 cm, BC = 15 cm, BD = 12 cm and CD = 9 cm. The area of quad ABCD is

Philoid · Accepted Answer

Given:

AC = 17 cm

BC = 15 cm

BD = 12 cm

CD = 9 cm.

∠ABC = 90°

∠BDC = 90°

In ∆ABC,

Using Pythagoras theorem,

AB² + BC² = AC²

⇒ AB² = AC²- BC²

⇒ AB = √( AC²- BC²)

⇒ AB = √( 17²- 15²)

⇒ AB = √(289-225)

⇒ AB = √64

⇒ AB = 8 cm

Therefore,

Area of ∆ABC = 1/2 × AB × BC

= 1/2 × 8 × 15

= 60 cm²

And,

In ∆BDC,

Area of ∆BDC = 1/2 × BD × DC

= 1/2 × × 12 × 9

= 54 cm²

Therefore,

Area of quadrilateral ABCD = Area of ∆ABC + Area of ∆BDC

= 60 cm² + 54 cm²

= 114 cm²