Question

AR=6cm,RT=5cm,and angle ART=70 degree what is the area of the parallelogram

Answer 1

If AR=6cm, RT=5cm and angle ART=70° then the area of the parallelogram is 28.14 cm².

Step-by-step explanation:

Referring to the figure attached below, let’s make some constructions and solve it accordingly:

Draw a perpendicular from vertex A intersecting ST of parallelogram ARTS at B such that angle ABT = 90° and AB becomes the perpendicular height of the parallelogram ARTS.  

It is given that,

AR = 6 cm

RT = 5 cm

∠ART = 70°

We know that a parallelogram has two pairs of parallel sides and the opposite sides or opposite angles of a parallelogram are of equal to each other.

Therefore, we have

AR // ST so, AR = ST = 6 cm  ..... [opposite sides]

AS // RT so, AS = RT = 5 cm  ..... [opposite sides]

∠ART = ∠AST = 70°  .... [opposite angles]

Now, consider ∆ASB and applying trigonometry properties of triangles, we get

sin θ = $\frac{Perpendicular}{Hypotenuse} = \frac{AB}{AS}$

⇒ sin 70° = $\frac{AB}{5}$

⇒ AB = 0.939 * 5

⇒ AB = 4.69 cm

Thus,  

The area of the parallelogram ARTS is given by,

= base * height

= ST * AB

substituting base = ST 6 cm and height = AB = 4.69 cm

= 6 * 4.69

= 28.14 cm²

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