Question

the sides of a triangle measures 13 cm, 14 cm and 15 cm find its area


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Answer 1

• Area of triangle is 84 cm².

Step-by-step explanation:

Here, we will use Heron's formula for area of triangle.

Heron's formula is

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

Where,

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

Now,

Given that,

Sides of triangle are 13 cm, 14 cm, 15 cm.

So,

Semi-perimeter = Perimeter of triangle/2

= 13 + 14 + 15/2

= 42/2

= 21

Semi-perimeter of triangle is 21 cm.

According to question:

$\sf \longrightarrow Area_{(Triangle)} =$ √21 × (21 - 13)(21 - 14)(21 - 15)

$\sf \longrightarrow Area_{(Triangle)} =$ √21 × 8 × 7× 6

$\sf \longrightarrow Area_{(Triangle)} =$ √3 × 7 × 2 × 2 × 2 × 7 × 2 × 3

$\sf \longrightarrow Area_{(Triangle)} =$ 3 × 7 × 2 × 2

$\longrightarrow \purple{\boxed{\sf \bold{Area_{(Triangle)} = 84}}\star}$

Therefore,

Area of triangle is 84 cm².

Answer 2

Step-by-step explanation:

Question

The sides of a triangle measures 13 cm, 14 cm and 15 cm find its area

Given

Sides of 3 triangles

1. 13 cm
2. 14 cm
3. 15 cm

Formula

Heron's formula we have to use here

$\pink{ \bigstar} \underline{ \boxed{ \sf{ \pink{ \sqrt{s(s - a)(s - b)(s - c)}}}}}$

Here,

• S is the semi-perimeter of triangle
• A,B,C are the three sides of the triangle

$: \: = > semi \: perimeter = \: \dfrac{perimeter \: of \: triangle}{2}$

= 13 + 14 + 15/2

= 42 /2

= 21

So, semi perimeter of the triangle is 21 cm

According to the question

$\underline{ \boxed{ \sf{ \pink{↦</p><p>Area(Triangle)= \sqrt{21 \times (21 - 13)(21 - 14)(21 - 15)}}}}}$

$\underline{ \boxed{ \sf{ \pink{↦</p><p>Area(Triangle)= \sqrt{21 \times (8) \times (7) \times (6 )}}}}}$

$\underline{ \boxed{ \sf{ \pink{↦</p><p>Area(Triangle)= \sqrt{3 \times 7\times 2 \times 2 \times 2 \times 7 \times 2 \times 3}}}}}$

$\underline{ \boxed{ \sf{ \pink{↦</p><p>Area(Triangle)= \sqrt{3 \times 7\times 2 \times 2 }}}}}$

$\underline{ \boxed{ \sf{ \purple{↦</p><p>Area(Triangle)= \bf84 }}}} \purple{ \bigstar}$

•°• Area of triangle is 84 cm²

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