Question

Trigonometry, how would I find the area of this parallelogram?

Answer 1

in∆BDC

use sine rule for area

`\\ \rm\rightarrowtail (1)/(2)absinC`

`\\ \rm\rightarrowtail (1)/(2)(12)(15)sin117`

`\\ \rm\rightarrowtail 90(0.89)`

`\\ \rm\rightarrowtail 80.1m^2`

• Area of parallelogram=2(80.1)=160.2m^2

Answer 2

A ≈ 160 cm²

Explanation:

the area (A) of a parallelogram given adjacent sides a and b and angle Θ between them is

A = absinΘ

here a = 12 , b = 15 and Θ = 117° , then

A = 12 × 15 × sin117° ≈ 160 cm²( to the nearest cm² )