Question

Sides of triangle are 11m, 15m, 6m. It's Semi Perimeter is 16m .
Find the area of triangle using heron's formula

plz answer.
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Answer 1

Answer:

By Heron's formula, we have area of triangle

=

S(S−a)(S−b)(S−c)

Here, S=

2

11+15+16

=

2

42

=21cm

∴ Area of triangle =

21(10)(6)(5)

=30

7

sq cm

Also, Area of triangle =

2

1

×base×height

∴ height =

base

2×area

=

8

30

7

=

4

15

7

cm

Answer 2

Answer :-

• Area of Triangle = 20√2 sq.m.

Explanation :-

Given :

• Sides of Triangle = 11 m, 15 m and 6 m.

• Semi Perimeter = 16 m.

To Find :

• Area of Triangle.

Solution :

We know that,

$\underline{\boxed{\sf\red{Area \: of \: Triangle = \sqrt{s(s - a)(s - b)(s - c)} }}}$

Here,

• a = 11 m.
• b = 15 m.
• c = 6 m.
• s = 16 m.

$\implies\sf{Area = \sqrt{16(16 - 11)(16 - 15)(16 - 6)} }$

$\implies\sf{Area = \sqrt{16 \times 5 \times 1 \times 10} }$

$\implies\sf{Area = \sqrt{2 \times 2 \times 2 \times 2 \times 5 \times 1 \times 5 \times 2} }$

$\implies\sf{Area = 5 \times 2 \times 2\sqrt{1 \times 2} }$

$\implies\boxed{\sf{\green{Area = 20 \sqrt{2} \: {m}^{2} }}}$

Therefore, Area of Triangle = 20√2 sq.m.

Note :-

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