Question

Find area of the triangle if its perimeter is 32 cms, if length of its two sides is
8 cms and 11 cms respectively,​

Answer 1

Answer:

13 cm

Step-by-step explanation:

perimeter of a triangle = side₁ + side₂ + side₃

⇒  32cm = 8cm + 11cm + $required\ side$

⇒  32cm = 19cm + $required\ side$

∴ $required\ side$ = 32cm - 19 cm = 13 cm

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Answer 2

Given:

✰ The length of two sides of a triangle are 8 cm and 11 cm respectively.

✰ The perimeter of a triangle = 32 cm

To find:

✠ The area of a triangle

Solution:

❖ Let's understand the concept first! First we will find the third side of triangle by using formula to calculate the perimeter and then semi perimeter because we will find area by using Heron's formula. At last, after finding the third side calculate the area of a triangle using Heron's formula.

Let's find out...

Let a, b, c be the length of sides of a given triangle,

and 2s be the perimeter of a triangle.

✭ Perimeter of triangle = a + b + c ✭

Now,

⟹ a + b + c = 2s

⟹ 8 + 11 + c = 32

⟹ 19 + c = 32

⟹ c = 32 - 19

⟹ c = 13 cm

Now, we know it's Semi-perimeter

• Semi-perimeter = Perimeter/2
• Semi-perimeter = 32/2
• Semi-perimeter = 16 cm

Using Heron's formula,

✭ Area of Triangle = √s(s - a) ( s - b ) ( s - c )✭

Putting the values,

➤ Area of Triangle = √16(16 - 8) ( 16 - 11 ) ( 16 - 13 )

➤ Area of Triangle = √16(8) ( 5 ) ( 3 )

➤ Area of Triangle = √16 × 8 × 5 × 3

➤ Area of Triangle = √2 × 8 × 8 × 5 × 3

➤ Area of Triangle = √2 × 8 × 8 × 5 × 3

➤ Area of Triangle = 8√2 × 5 × 3

➤ Area of Triangle = 8√30

∴ The area of Triangle = 8√30 cm²

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