Question

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

Options

• 102 cm²

• 114 cm²

• 95 cm²

• 57 cm²

Answer 1

In the given figure ABDC is a quadrilateral in which ∠ABC = 90°, ∠BDC = 90°, AC = 17 cm, BC = 15 cm, BD = 12 cm and CD = 9 cm. The area of quad. ABDC is 114 cm².

Explanation:

Since ∠ABC = 90° and AC = 17, BC = 15.

By Pythagoras `AB = sqrt(AC^2 - BC^2)` 

= `sqrt(289 - 225)`

= 8

Triangle ABC area = `1/2 xx BC xx AB`

= `1/2 xx 15 xx 8`

= 60 cm²

Triangle BDC is right-angled with legs BD = 12 and CD = 9.

So its area = `1/2 xx 12 xx 9` 

= 54 cm²

Quadrilateral ABDC = Area (ABC) + Area (BDC) 

= 60 + 54

= 114 cm²