6. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Share
6. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Given: An isosceles triangle has Perimeter 30 cm. & each of the equal sides of triangle is 12 cm.
Need to find: The area of the triangle?
⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀
So, we will use Heron's Formula to find the Area of Triangle (let's say ∆ABC).
✇ If the perimeter of given isosceles triangle is 30 cm then the semi perimeter of the isosceles triangle would be 15 cm. i.e ( s ) = 15 cm.
⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀
⠀
( I ) Finding third Side :
» As We know that, Perimeter of triangle is equal to sum of all sides of triangle. & The perimeter is Given that is 30 cm. Therefore:
∴ Hence, third side of the triangle is 6 cm.
⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀
( II ) Area of Triangle :
⠀⠀⠀⠀⠀⠀
Question:
Answer:
Explanation:
Given that:
To Find:
Solution:
We know that,
✪ Perimeter of ∆ = Sum of all sides ✪
Putting values in formula we get,
➻ 12 + 12 + Third side = 30
➻ Third side + 24 = 30
➻ Third side = 30 - 24
➻ Third side = 6 cm
We know that,
✪ ✪
Putting values in formula we get,
➻
➻ s = 15 cm
According to heron's formula we know that,
✪ Area of ∆ = √[s(s - a)(s - b)(s - c)] ✪
Putting all values in formula we get,
➻ Area of ∆ = √[15(15 - 12)(15 - 12)(15 - 6)]
➻ Area of ∆ = √(15 × 3 × 3 × 9)
➻ Area of ∆ = √(15 × 9 × 9)
➻ Area of ∆ = 9√15 cm²
∴ Area of ∆ is 9√15 cm².
⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━
Know more :-
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬