Question

sides of triangle are 45cm, 39cm, 42cm find its area​

Answer 1

Given:

• Sides of a triangle are 45 cm, 39 cm, 42 cm

To calculate:

• Area of the triangle.

Calculation:

Here, we are provided with the sides of the triangle, and we need to calculate the area of triangle. So, firstly we need to find the semi-perimeter of the triangle.

Formula -

$\dag{ \underline{ \boxed{ \tt{ \blue{Semi-perimeter_{(Triangle)} = \dfrac{a + b + c}{2} }}}}}$

Where, a, b & c are the sides of the triangle. Also the provided values are,

• a = 45 cm
• b = 39 cm
• c = 42 cm

D I A G R A M :

$\setlength{\unitlength}{2.5mm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(8,17)\qbezier(0,0)(0,0)(18,0)\qbezier(18,0)(18,0)(8,17)\put(8,17.8){\sf A}\put( - 1, - 1){\sf B}\put(18,-1){\sf C}\put(8, - 1.5){\sf 39 \: cm}\put(15,8.1){\sf 42 \: cm}\put( - 0,8.1){\sf 45 \: cm}\end{picture}$

Now, as per the formula, let's calculate the semi-perimeter of the triangle.

Formula :

$\dag{ \underline{ \boxed{ \tt{ \blue{Semi-perimeter_{(Triangle)} = \dfrac{a + b + c}{2} }}}}}$

Plugging the values,

$\tt Semi-perimeter_{(Triangle)} = \dfrac{45 + 39 + 42}{2}$

On adding the numbers,

$\tt Semi-perimeter_{(Triangle)} = \dfrac{126}{2}$

Cancelling the numbers,

$\tt Semi-perimeter_{(Triangle)} = \cancel \dfrac{126}{2}$

So, the semi-perimeter of triangle is,

$\tt \red{Semi-perimeter_{(Triangle)} = 63 \: cm}$

According to the Question,

Let's calculate the area of triangle. For calculating the area of triangle, we will use Heron's Formula for it,

• $\underline{\underline{\boxed{ \green{ \tt{Area_{(Triangle)} = \sqrt{s(s - a)(s - b)(s - c)} }}}}}$

Plugging the values in the equation,

$\rm Area_{(Triangle)} = \sqrt{63(63 - 45)(63 - 39)(63 - 42)}$

After evaluating,

$\rm Area_{(Triangle)} = \sqrt{63 \times 18 \times 24 \times 21}$

On multiplying the numbers,

$\rm Area_{(Triangle)} = \sqrt{571536}$

On removing the square root,

$\dashrightarrow \rm{\pink{Area_{(Triangle)} = 756 \: cm^2}}$

Therefore, area of triangle is 756 cm².

Answer 2

Given :

• 1st side of Triangle = 45cm
• 2nd side of Triangle = 39cm
• 3rd side of Triangle = 42cm

To Find :

• Area of Triangle

Solution :

✰ As we know that, if three sides of a triangle are given then we have to use Heron's Formula to find the area of the Triangle. Now in this question, Three sides are given so firstly we will find the semi perimeter of the Triangle and then we will apply Heron's Formula to find the area of the Triangle.

⠀

⠀⠀⠀⟼⠀⠀⠀s = a + b + c/2

⠀⠀⠀⟼⠀⠀⠀s = 45 + 39 + 42/2

⠀⠀⠀⟼⠀⠀⠀s = 45 + 81/2

⠀⠀⠀⟼⠀⠀⠀s = 126/2

⠀⠀⠀⟼⠀⠀⠀s = 63cm

⠀

Thus semi perimeter of Triangle is 63cm

________________

⠀

✰ Now, We will find the area of the Triangle using Heron's Formula.

➟ √s (s - a) (s - b) (s - c)

➟ √63 (63 - 45) (63 - 39) (63 - 42)

➟ √63 × 18 × 24 × 21

➟ √1134 × 504

➟ √571536

➟ 756cm²

⠀

Thus Area of Triangle is 756cm²

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