Question

Find area of a triangle, two of it's sides are 18cm and 10cm and perimeter is 42​

Answer 1

Question

Find area of a triangle, two of it's sides are 18cm and 10cm and perimeter is 42 cm

Solution

Given:-

• Perimeter of triangle = 42cm
• Side are triangle 18 cm , 10 cm

Find:-

• Area of triangle ?

Explanation

Using Formula

☛ perimeter of triangle = Sum of all side

☛ Area of triangle = 1/2 * (Base) * Perpendicular

In ∆ABC ,

• AB = 18 cm ,
• BC = 10 cm
• CA = ?

So,

➥ perimeter of triangle = 42

➥ AB + BC + CA = 42

➥ 18 + 10 + CA = 42

➥ CA = 42 - 28

➥ CA = 14 cm.

Now, Calculate Area of triangle

let,

☛Semi perimeter (S) =( AB + BC + CA)/2

➥ Semi perimeter(S) = (18+10+14)/2

➥ Semi perimeter(S) = 42/2

➥ Semi perimeter(S) = 21

By, Heron's formula

☛ Area = √[S(S-AB)(S-BC)(S-CA)]

Keep above all values

➥ Area of triangle = √[21(21-18)(21-10)(21-14)]

➥ Area of triangle = √[21 × 3 × 11 × 7 ]

➥ Area of triangle = √[ 7 × 3 × 3 × 11 × 7]

➥ Area of triangle = (7 × 3 ).√11

➥ Area of triangle = 21√11 cm²

Thus

• Area of triangle = 21√11 cm².

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