Question

In ΔXYZ, side y = 5 cm, side z = 6 cm, and X = 40°. Find the area of ΔXYZ.

A) 7.5 cm2

B) 9.6 cm2

C) 15.0 cm2

D) 19.3 cm2

Answer 1

The Required area of Δ
`XYZ` is
`9.6 \ cm^(2)`.

Explanation:

Diagram of given scenario is shown below.

Given that,

`XY=5\ cm`,
`XZ=6\ cm` and
`\angle X=40`°

To find : The area of Δ
`XYZ`.

So, from the question

Area of triangle when two sides and one angle (between two known sides) are given
`(Area) = (product \ of \ known\ side * Sin\angle m)/(2)` , where
`\angle m` is the given angle.

Substituting the given values in above to find area of Δ
`XYZ` we get,

`Ar(\triangle XYZ) = (5*6* Sin\angle40)/(2)`

`= 15*0.642788`

`= 9.6 \ cm^(2)`

Therefore, The Required area of Δ
`XYZ` is
`9.6 \ cm^(2)`.