Question

In a ΔABC, if a = `sqrt(2)` x and b = 2y and ∠C = 135°, then the area of triangle is ______.

Options

• xy

• `sqrt(2)` xy

• `1/(2sqrt(2))` xy

• `2sqrt(2)` xy

Answer 1

In a ΔABC, if a = `sqrt(2)` x and b = 2y and ∠C = 135°, then the area of triangle is xy.

Explanation:

A(ΔABC) = `1/2 "ab" sin "C"`

= `1/2(sqrt(2)x)(2y) sin 135° `

= `1/2(sqrt(2)x)(2y) sin (90^circ + 45^circ)`

= `sqrt(2)xy xx cos 45^circ`

= `sqrt(2)xy xx 1/sqrt(2)` = xy