Question

By Heron's formula find area of triangle having sides 4cm, 6cm and 8 cm

Answer 1

Answer:

S=a + b + c ÷ 2

S=4+6+8/2

 =9

Area of Triangle = $\sqrt{s(s-a)(s-b)(s-c)$

                           =$\sqrt{9(9-4)(9-6)(9-8)$

                           =$\sqrt{9*5*3*1$

                           =$3\sqrt{15$

Step-by-step explanation:

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Answer 2

Answer :

›»› The area of a triangle is 11.61 cm².

Step-by-step explanation :

Given :

• The three sides of a triangle is 4 cm, 6cm and 8 cm.

To Find :

• Area of triangle = ?

Formula required :

Formula to calculate the Semi perimeter is given by,

→ s = a + b + c/2.

Here,

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

Units,

• The unit of semi-perimeter is cm.
• The unit of three sides is cm.

Formula to calculate the area of triangle is given by,

→ Area of triangle = √{s(s - a)(s - b)(s - c)}.

Here,

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

Units,

• The unit of semi-perimeter is cm.
• The unit of three sides is cm.

Solution :

We know that, if we are given with the three sides of a triangle then we have the required formula, that is,

→ s = a + b + c/2.

By using the formula to calculate the semi-perimeter of triangle and substituting all the given values in the formula, we get :

→ s = 4 + 6 + 8/2

→ s = 10 + 8/2

→ s = 18/2

→ s = 9.

∴ The semi-perimeter of a triangle is 9 cm.

Now,

We know that, if we are given with the semi-perimeter of triangle and three sides of triangle then we have the required formula, that is,

→ Area of triangle = √{s(s - a)(s - b)(s - c)}.

By using the formula to calculate the area of triangle and substituting all the given values in the formula, we get :

→ Area of triangle = √{9(9 - 4)(9 - 6)(9 - 8)}

→ Area of triangle = √{9(5)(9 - 6)(9 - 8)}

→ Area of triangle = √{9(5)(3)(9 - 8)}

→ Area of triangle = √{9(5)(3)(1)}

→ Area of triangle = √(9 * 5 * 3 * 1)

→ Area of triangle = √(45 * 3 * 1)

→ Area of triangle = √(135 * 1)

→ Area of triangle = √135

→ Area of triangle = 11.61.

Hence, the area of triangle is 11.61 cm².

Answer 3

Answer :

›»› The area of a triangle is 11.61 cm².

Step-by-step explanation :

Given :

• The three sides of a triangle is 4 cm, 6cm and 8 cm.

To Find :

• Area of triangle = ?

Formula required :

Formula to calculate the Semi perimeter is given by,

→ s = a + b + c/2.

Here,

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

Units,

• The unit of semi-perimeter is cm.
• The unit of three sides is cm.

Formula to calculate the area of triangle is given by,

→ Area of triangle = √{s(s - a)(s - b)(s - c)}.

Here,

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

Units,

• The unit of semi-perimeter is cm.
• The unit of three sides is cm.

Solution :

We know that, if we are given with the three sides of a triangle then we have the required formula, that is,

→ s = a + b + c/2.

By using the formula to calculate the semi-perimeter of triangle and substituting all the given values in the formula, we get :

→ s = 4 + 6 + 8/2

→ s = 10 + 8/2

→ s = 18/2

→ s = 9.

∴ The semi-perimeter of a triangle is 9 cm.

Now,

We know that, if we are given with the semi-perimeter of triangle and three sides of triangle then we have the required formula, that is,

→ Area of triangle = √{s(s - a)(s - b)(s - c)}.

By using the formula to calculate the area of triangle and substituting all the given values in the formula, we get :

→ Area of triangle = √{9(9 - 4)(9 - 6)(9 - 8)}

→ Area of triangle = √{9(5)(9 - 6)(9 - 8)}

→ Area of triangle = √{9(5)(3)(9 - 8)}

→ Area of triangle = √{9(5)(3)(1)}

→ Area of triangle = √(9 * 5 * 3 * 1)

→ Area of triangle = √(45 * 3 * 1)

→ Area of triangle = √(135 * 1)

→ Area of triangle = √135

→ Area of triangle = 11.61.

Hence, the area of triangle is 11.61 cm².