Question

find the area of a triangle whose sides are of length 20 cm ,12 cm, and 16 cm, using heron's formula. Also find its perimeter.​

Answer 1

Answer:

Step-HERON'S FORMULA

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Area of a triangle of sides a , b & c is :

√( s(s-a)(s-b)(s-c) )

where s=(a+b+c)/2

ln given trangle , s=(20+12+16)/2=48/2=24

Thus area of given triangle =

√(24(24-20)(24-12)(24-16))

=√(24×4×12×8)

=√9216

=96

Thus area of triangle of sides 20cm ,12cm and 16cm is 96cm^2-step

explanation:

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Answer 2

Answer:

• Area of triangle is 96 cm².
• Perimeter of triangle is 48 cm.

Step-by-step explanation:

Given :-

• Sides of triangle are 20 cm, 12 cm and 16 cm.

To find :-

• Area of triangle.
• Perimeter of triangle.

Solution :-

We know,

Heron's formula is :

Area of triangle = √s(s - a)(s - b)(s - c)

Where,

• a, b and c are sides of triangle.
• s is semi-perimeter of triangle.

So,

Semi-perimeter = Perimeter/2

$\longrightarrow$ Semi-perimeter = 20 + 12 + 16/2

$\longrightarrow$ Semi-perimeter = 48/2

$\longrightarrow$ Semi-perimeter = 24

Semi-perimeter of triangle is 24 cm.

Now, Put all values in area formula :

$\longrightarrow$ Area = √24 × (24 - 20)(24 - 12)(24 - 16)

$\longrightarrow$ Area = √24 × 4 × 12 × 8

$\longrightarrow$ Area = √2 × 2 × 2 × 3 × 2 × 2 × 2 × 2 × 3 × 2 × 2 × 2

$\longrightarrow$ Area = 2 × 2 × 2 × 2 × 2 × 3

$\longrightarrow$ Area = 96

Thus,

Area of triangle is 96 cm².

Now,

Perimeter of triangle= Sum of all sides

$\longrightarrow$ Perimeter = 20 + 12 + 16

$\longrightarrow$ Perimeter = 48

Therefore,

Perimeter of triangle is 48 cm.