Question

find the the area of triangle two sides of each are 8 cm and 11cm and the perimeter is is 32 CM ​

Answer 1

Step-by-step explanation:

Answer and formula in the attachment.

Answer 2

Given :

• Two sides of a triangle are 8 cm and 11 cm.
• Perimeter of the triangle = 32 cm.

To Find :

The area of the triangle.

Solution :

Analysis :

Here we first have to find the third side of the triangle using the perimeter of the triangle. Then using Heron's Formula we can find the area of the triangle.

Required Formula :

• Perimeter = a + b + c

• Heron's Formula = √[s(s - a)(s - b)(s - c)]

where,

• a = First Side
• b = Second Side
• c = Third Side
• s = Semiperimeter

Explanation :

We know that if we are given the two sides of a triangle and its perimeter and is asked to find the third side then our required formula is,

Perimeter = a + b + c

where,

• Perimeter = 32 cm
• a = 8 cm
• b = 11 cm
• c = c cm

Using the required formula and substituting the required values,

⇒ Perimeter = a + b + c

⇒ 32 = 8 + 11 + c

⇒ 32 = 19 + c

⇒ 32 - 19 = c

⇒ 13 = c

∴ Third Side = 13 cm.

Semiperimeter :

We know that,

Semiperimeter = Perimeter/2

where,

• Perimeter = 32 cm

⇒ Semiperimeter = 32/2

⇒ Semiperimeter = 16

∴ Semiperimeter = 16 cm.

Now,

If we are given the three sides of a triangle and it semiperimeter and is asked to find the area then the formula is,

By using Heron's Formula,

Area = √[s(s - a)(s - b)(s - c)]

where,

• a = 8 cm
• b = 11 cm
• c = 13 cm
• s = 16 cm

Using the required formula and substituting the required values,

⇒ Area = √[s(s - a)(s - b)(s - c)]

⇒ Area = √[16(16 - 8)(16 - 11)(16 - 13)]

⇒ Area = √[16(8)(5)(3)]

⇒ Area = √[16 × 8 × 5 × 3]

⇒ Area = √[8 × 2 × 8 × 5 × 3]

⇒ Area = √[8 × 8 × 2 × 5 × 3]

⇒ Area = √8² × √[2 × 5 × 3]

⇒ Area = 8 × √[2 × 5 × 3]

⇒ Area = 8√30

∴ Area = 8√30 cm².

The area of the rectangle is 8√30.