1.

Calculate the area andperimeter ofthe giventriangle ​

Answer»

Answer:

Area = 20.79cm²

Perimeter = 25.86cm

Step-by-step explanation:

Let's find the THIRD angle first,

⇒ ∠ x = 180 - 60

⇒ ∠ x = 120°

Now let's find the third side of the TRIANGLE below 12CM using sine rule,

⇒ 12 / sin 120 = side₁ / sin 30

⇒ ( 12 × sin 30 ) / sin 120 = side₁

⇒ 6.928cm = side₁

Now let's APPLY the area formula,

⇒ Area = 1/2 × ( a × b × sin C )

⇒ Area = 1/2 × ( 12 × 6.93 × sin 30 )

⇒ Area = 1/2 × 41.6

⇒ Area = 20.79cm²

Now let's find the third side to find the perimeter later,

⇒ 12 / sin 120 = side₂ / sin 30

⇒ ( 12 × sin 30 ) / sin 120 = side₂

⇒ side₂ = 6.93cm

Now let's find the perimeter,

⇒ Perimeter = 2 ( 6.93 ) + 12

⇒ Perimeter = 13.86 + 12

⇒ Perimeter = 25.86cm

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