Find the area of triangle if sides of triangle and 12 cm 15cm and 21cm
Answers
Answer: Using Heron's formula
The sides of a triangle is 12cm ,15cm ,21cm
So, Semi perimeter ( s ) = sum of all sides = 12 +15 +21 = 24
2 2
√s ( s-a) ( s-b) (s-c) = √24(24-12) (24-15) (24-21) = √24 ( 12 ) ( 9 ) ( 3 )
√ 2 x 3 x 2 x 2 x 2 x 3 x 2 x 3 x 3 x 3 = 2 x 3 x 2 x 3 √ 2 x 3 = 36√6cm² ANS
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GIVEN :-
- Sides of Triangle are 12 cm, 15 cm, 21 cm.
TO FIND :-
- The Area of Triangle.
SOLUTION :-
★ From the question we have ,
- a = 12 cm.
- b = 15 cm.
- c = 21 cm.
★ Semi - Perimeter (s) = (a + b + c)/2
➺ s = (12 + 15 + 21)/2
➺ s = 48/2
➺ s = 24.
❏ Hence semi - perimeter (s) = 24 cm.
★ Now as we know that,
➺ Area of △ = √s(s - a) (s - b) (s - c).
★ From the above Formula we have,
- s - a = 24 - 12 = 12.
- s - b = 24 - 15 = 9.
- s - c = 24 - 21 = 3.
★ Now substitute the above values.
➺ Area of △ = √s(s - a) (s - b) (s - c).
➺ √24 × 12 × 9 × 3
➺√7776
➺ 36√6
➺ 88 . 18 cm².
❏ Hence the Area of △ is 88.18 cm² or 36√6 cm².