Question

❝ Calculate ❞
If the length of the sides of a triangle ABC are 4 in, 3 in, and 5 in. Calculate its area.

Answer 1

★ Given:-      

• ➳ Side a = 4 in
• ➳ Side b = 3 in
• ➳ Side c = 5 in

★ To find:-      

• ➯ The area of the triangle.

★ Solution:-      

Here we have given that the length of the sides of a triangle ABC are 4 in, 3 in, and 5 in and we have to find out the area of the triangle.

To find out the area of the triangle we need a semi-perimeter of the triangle so firstly we will find out the semi-perimeter of the triangle by using the formula.

• $\large\boxed{\tt{Semi\:-\:perimeter\:=\:\left(\:\dfrac{a\:+\:b\:+\:c}{2}\:\right)}}$

Where,

• ➺ Side a = 4 in
• ➺ Side b = 3 in
• ➺ Side c = 5 in

♡ Calculating the semi-perimeter ♡

$\qquad\tt{:\implies\:Semi\:-\:perimeter\:=\:\left(\:\dfrac{a\:+\:b\:+\:c}{2}\:\right)}$

$\qquad\tt{:\implies\:Semi\:-\:perimeter\:=\:\left(\:\dfrac{4\:+\:3\:+\:5}{2}\:\right)}$

$\qquad\tt{:\implies\:Semi\:-\:perimeter\:=\:\left(\:\dfrac{7\:+\:5}{2}\:\right)}$

$\qquad\tt{:\implies\:Semi\:-\:perimeter\:=\:\left(\:\dfrac{12}{2}\:\right)}$

$\qquad\tt{:\implies\:Semi\:-\:perimeter\:=\:6\:units}$

. ° . Thus the semi-perimeter of the triangle is 6 units.

                         _______________

Now, so that we have calculated the semi-perimeter of the triangle we can find out the area of the triangle by using the formula.

• $\large\boxed{\tt{Area\:_{(TRIANGLE)}\:=\:\sqrt{s\:(\:s\:-\:a\:)\:(\:s\:-\:b\:)\:(\:s\:-\:c\:)\:} }}$

Where,

• ➽ Semi- perimeter = 6 units
• ➽ Side a = 4 units
• ➽ Side b = 3 units
• ➽ Side c = 5 units

♡ Calculating the area ♡

$\qquad\tt{:\implies\:Area\:_{(TRIANGLE)}\:=\:\sqrt{s\:(\:s\:-\:a\:)\:(\:s\:-\:b\:)\:(\:s\:-\:c\:)\:} }$

$\qquad\tt{:\implies\:Area\:_{(TRIANGLE)}\:=\:\sqrt{\:6\:(\:6\:-\:4\:)\:(\:6\:-\:3\:)\:(\:6\:-\:5\:)\:} }$

$\qquad\tt{:\implies\:Area\:_{(TRIANGLE)}\:=\:\sqrt{\:6\:(\:2\:)\:(\:3\:)\:(\:1\:)\:} }$

$\qquad\tt{:\implies\:Area\:_{(TRIANGLE)}\:=\:\sqrt{\:6\:\times\:2\:\times\:3\:\times\:1\:} }$

$\qquad\tt{:\implies\:Area\:_{(TRIANGLE)}\:=\:\sqrt{\:12\:\times\:3\:\times\:1\:} }$

$\qquad\tt{:\implies\:Area\:_{(TRIANGLE)}\:=\:\sqrt{\:36\:\times\:1\:} }$

$\qquad\tt{:\implies\:Area\:_{(TRIANGLE)}\:=\:\sqrt{\:36\:}}$

$\qquad\tt{:\implies\:Area\:_{(TRIANGLE)}\:=\:6\:in\:^{2}}$

. ° . Thus the area of the triangle is 6 in².

                     _____________

★ Explore more:-        

• https://brainly.in/question/45333877
• https://brainly.in/question/45344522
• https://brainly.in/question/44734921
• https://brainly.in/question/44671032
• https://brainly.in/question/44566679
• https://brainly.in/question/44274784

Answer 2

Answer:

★ Given:-

★ Given:- ➳ Side a = 4 in

★ Given:- ➳ Side a = 4 in➳ Side b = 3 in

★ Given:- ➳ Side a = 4 in➳ Side b = 3 in➳ Side c = 5 in

★ Given:- ➳ Side a = 4 in➳ Side b = 3 in➳ Side c = 5 in★ To find:-

★ Given:- ➳ Side a = 4 in➳ Side b = 3 in➳ Side c = 5 in★ To find:- ➯ The area of the triangle.

★ Given:- ➳ Side a = 4 in➳ Side b = 3 in➳ Side c = 5 in★ To find:- ➯ The area of the triangle.★ Solution:-

★ Given:- ➳ Side a = 4 in➳ Side b = 3 in➳ Side c = 5 in★ To find:- ➯ The area of the triangle.★ Solution:- Here we have given that the length of the sides of a triangle ABC are 4 in, 3 in, and 5 in and we have to find out the area of the triangle.

★ Given:- ➳ Side a = 4 in➳ Side b = 3 in➳ Side c = 5 in★ To find:- ➯ The area of the triangle.★ Solution:- Here we have given that the length of the sides of a triangle ABC are 4 in, 3 in, and 5 in and we have to find out the area of the triangle.To find out the area of the triangle we need a semi-perimeter of the triangle so firstly we will find out the semi-perimeter of the triangle by using the formula.

★ Given:- ➳ Side a = 4 in➳ Side b = 3 in➳ Side c = 5 in★ To find:- ➯ The area of the triangle.★ Solution:- Here we have given that the length of the sides of a triangle ABC are 4 in, 3 in, and 5 in and we have to find out the area of the triangle.To find out the area of the triangle we need a semi-perimeter of the triangle so firstly we will find out the semi-perimeter of the triangle by using the formula.Where,

★ Given:- ➳ Side a = 4 in➳ Side b = 3 in➳ Side c = 5 in★ To find:- ➯ The area of the triangle.★ Solution:- Here we have given that the length of the sides of a triangle ABC are 4 in, 3 in, and 5 in and we have to find out the area of the triangle.To find out the area of the triangle we need a semi-perimeter of the triangle so firstly we will find out the semi-perimeter of the triangle by using the formula.Where,➺ Side a = 4 in

★ Given:- ➳ Side a = 4 in➳ Side b = 3 in➳ Side c = 5 in★ To find:- ➯ The area of the triangle.★ Solution:- Here we have given that the length of the sides of a triangle ABC are 4 in, 3 in, and 5 in and we have to find out the area of the triangle.To find out the area of the triangle we need a semi-perimeter of the triangle so firstly we will find out the semi-perimeter of the triangle by using the formula.Where,➺ Side a = 4 in➺ Side b = 3 in

➺ Side c = 5 in

➺ Side c = 5 in♡ Calculating the semi-perimeter ♡

➺ Side c = 5 in♡ Calculating the semi-perimeter ♡Where,

➺ Side c = 5 in♡ Calculating the semi-perimeter ♡Where,➽ Semi- perimeter = 6 units

➺ Side c = 5 in♡ Calculating the semi-perimeter ♡Where,➽ Semi- perimeter = 6 units➽ Side a = 4 units

➺ Side c = 5 in♡ Calculating the semi-perimeter ♡Where,➽ Semi- perimeter = 6 units➽ Side a = 4 units➽ Side b = 3 units

➺ Side c = 5 in♡ Calculating the semi-perimeter ♡Where,➽ Semi- perimeter = 6 units➽ Side a = 4 units➽ Side b = 3 units➽ Side c = 5 units

➺ Side c = 5 in♡ Calculating the semi-perimeter ♡Where,➽ Semi- perimeter = 6 units➽ Side a = 4 units➽ Side b = 3 units➽ Side c = 5 units♡ Calculating the area ♡

➺ Side c = 5 in♡ Calculating the semi-perimeter ♡Where,➽ Semi- perimeter = 6 units➽ Side a = 4 units➽ Side b = 3 units➽ Side c = 5 units♡ Calculating the area ♡

➺ Side c = 5 in♡ Calculating the semi-perimeter ♡Where,➽ Semi- perimeter = 6 units➽ Side a = 4 units➽ Side b = 3 units➽ Side c = 5 units♡ Calculating the area ♡ . ° . Thus the area of the triangle is 6 in²