Question

Find the area of triangle whose sides are 17cm ,25cm 26cm​​

Answer 1

$\large \bf{ \underline{ \underline{Answer :}}}$

• Area of the triangle is 204 cm².

Elucidation:

Here, it's given that the sides of a triangle are 17 cm, 25 cm and 26 cm. And we are asked to calculate the area of the triangle.

Firstly, we need to calculate the semi-perimeter of the triangle, by using this formula :-

• $\boxed{ \rm{ \gray{s = \dfrac{a + b + c}{2}}}}$

And lastly, according to the question, we'll be calculating the area of triangle,

$\bullet$ To calculate the area of triangle, we'll be using the heron's formula (for triangle).

• $\boxed{\rm{ \gray { {Area}_{(Triangle)} = \sqrt{S(s - a)(s - b)(s - c) \: sq. \: unit } }}}$

Given:

• Sides of the triangle are 17 cm, 25 cm and 26 cm.

To Find:

• Area of the triangle.

Calculation:

~ Calculating the semi-perimeter of the triangle,

Here,

• a = 17 cm
• b = 25 cm
• c = 26 cm

Putting the values,

$\longrightarrow \sf \: s = \dfrac{a + b + c}{2} \\ \\ \\ \longrightarrow \sf \: s = \dfrac{17 + 25 + 26}{2} \\ \\ \\ \longrightarrow \sf \: s = \dfrac{68}{2} \\ \\ \\ \longrightarrow \sf \: s = \cancel\dfrac{68}{2} \\ \\ \\ \longrightarrow \boxed{ \sf{s = 34}} \: \blue{ \bigstar}$

Therefore, semi-perimeter of the triangle is 34 cm.

$\dag$ According to the Question,

~ Calculating the area of triangle,

By using this formula, we'll be calculating the area of triangle,

• $\boxed{\bf{ \red { {Area}_{(Triangle)} = \sqrt{S(s - a)(s - b)(s - c) \: sq. \: unit } }}}$

Putting the values,

$\longrightarrow \sf { {Area}_{(Triangle)} = \sqrt{S(s - a)(s - b)(s - c) \: }} \\ \\ \\ \longrightarrow \sf { {Area}_{(Triangle)} = \sqrt{34(34 - 17)(34 - 25)(34 - 26) \: }} \\ \\ \\ \longrightarrow \sf { {Area}_{(Triangle)} = \sqrt{34 \times 17 \times 9 \times 8 \: }} \\ \\ \\ \longrightarrow \sf { {Area}_{(Triangle)} = 2 \times 2 \times 17 \times 3 } \\ \\ \\ \longrightarrow \sf { {Area}_{(Triangle)} = 4 \times 51 } \\ \\ \\ \longrightarrow { \boxed{\sf { {Area}_{(Triangle)} = 204 \: cm^2 }}} \: \pink{ \bigstar}$

Therefore, area of triangle is 204 cm².

Answer 2

$\large{\bf{Answer :}}$

$~~~~~~~$

• Area of the triangle is 204 cm².

$~~~~~~~$

$~~~~~~~~~~~~~~$ _______________

$~~~~~~~~~~~~~~$ ★ Elucidation :

$~~~~~~~~~~~~~~$ _______________

$~~~~~~~$

Here,

• It's given that the sides of a triangle are 17cm , 25cm and 26cm. And we are asked to calculate the area of the triangle.

Firstly, we need to calculate the Semi - Perimeter of the triangle, by using the formula :

$~~~~~~~~$

• ${\underline{\boxed{\green{\sf{s = \frac{a + b + c}{2} }}}}}$

$~~~~~~~~$

And lastly, according to the question, we'll be calculating the area of triangle.

★ To calculate the area of triangle, we'll be using the heron's formula ( for triangle).

$~~~~~~~~$

• $\large\boxed{\sf\green{ Area_{(Triangle) } = \sqrt{S(s - a)(s - b)(s - c)sq. \: unit} }}$

$~~~~~~~~$

Given :-

$~~~~~~~~~$

• Sides of the triangle are 17cm , 25cm and 26cm.

$~~~~~~~~~$

To find :-

$~~~~~~~~$

• Area of the triangle

$~~~~~~~~~$

Solution :-

$~~~~~~~~~$

Calculation :

★ Calculation the Semi - Perimeter of the triangle.

Here,

• a = 17cm
• b = 25cm
• c = 26cm

$~~~~~~~$

$~~~~~~~~~~~~~~~~$$\large\dag$ Putting the values,

$~~~~~~~~$

$\implies$ $\large{\sf{s = \frac{a + b + c}{2} }}$

$~~~~~~~~$

$\implies$ $\large{\sf{s = \frac{17 + 25 + 26}{2} }}$

$~~~~~~~~$

$\implies$ $\large{\sf{s = \frac{68}{2}}}$

$~~~~~~~~$

$\implies$ $\large{\sf{s = \dfrac{\cancel{68}}{\cancel{2}}}}$

$~~~~~~~~$

$\implies$ ${\underline{\boxed{\purple{\sf{s = 34}}}}}$★

$~~~~~~~~$

Therefore,

$~~~~~~~~$

• Semi - Perimeter of the triangle is 34 cm.

$~~~~~~~~$

$~~~~~~~~~~~~~~~~~~~~~$ ___________________

$~~~~~~~~~~~~~~~~~~~~~$ ★ According to the question :

$~~~~~~~~~~~~~~~~~~~~~$ ___________________

$~~~~~~~~~$

$\large\dag$ Calculating the trianglearea of triangle :

$~~~~~~~~~$

★ By using this formula, we'll be calculating the area of formula :

$~~~~~~~~~~$

• $\large\boxed{\sf\green{Area_{(Triangle)} = \sqrt{S(s - a)(s - b)(s - c)sq. \: unit}}}$

$~~~~~~~~~~$

$~~~~~~~~~~~~~~~~$$\large\dag$ Putting the values,

$~~~~~~~~$

$\implies$ $\large{\sf{Area_{(Triangle)} = \sqrt{S(s - a)(s - b)(s - c)}}}$

$~~~~~~~~~~$

$\implies$ $\large{\sf{Area_{(Triangle)} = \sqrt{34(34 - 17)(34 -25)(34 -26)}}}$

$~~~~~~~~~$

$\implies$ $\large{\sf{Area_{(Triangle)} = \sqrt{34 \times 17 \times 9 \times 8} }}$

$~~~~~~~~~$

$\implies$

$\large{\sf{Area_{(Triangle)} = 2 \times 2 \times 17 \times 3}}$

$~~~~~~~~~$

$\implies$$\large{\sf{Area_{(Triangle)} = 4 \times 54}}$

$~~~~~~~~~$

$\implies$${\underline{\boxed{\purple{\sf{Area_{(Triangle)} = 204~cm²}}}}}$★

$~~~~~~~~$

$\large\dag$ Hence,

$~~~~~~~~$

• Therefore, area of triangle is 204 cm².