Question

The sides of the triangle are 56 cm, 60 cm, and 52 cm long. Then the area of the triangle is?

Answer 1

Sides of a triangle..

, a = 56, b = 60, c = 52

s = (a + b + c)/2

⇒ s = (56 + 60 + 52)/2

= 168/2 = 84.

Area of triangle = √s(s-a)(s-b)(s-c)

= √84(84-56)(84-60)(84-52)

= √84×28×24×32 =

1344cm2 ..Answer..

Answer 2

★ Assumption Needed:-    

Let the sides be,

• ➾  Side a = 56 cm
• ➾  Side b = 60 cm
• ➾  Side c = 52 cm

★ To Calculate:-    

• Area of the triangle.

★ Formula Used:-    

~Semi-Perimeter

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

Where,

• ➾  a = Length of side a
• ➾  b = Length of side b
• ➾  c = Length of side c

~Area of the triangle

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

Where,

• ➾  s = semi-perimeter
• ➾  a = 8 cm = Length of side a
• ➾  b = 42 cm = Length of side b
• ➾  c = 44 cm = Length of side c

★ Calculating:-      

Step1: Now we will find out the semi-perimeter so we will substitute the values in the formula. [ Semi-perimeter = a + b + c/2 ]

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

$\qquad\tt{:\implies\:Semi\:-\:perimeter\:=\:\left(\dfrac{56\:+\:60\:+\:52}{2}\right)}$

$\qquad\tt{:\implies\:Semi\:-\:perimeter\:=\:\left(\dfrac{168}{2}\right)}$

$\qquad\tt{:\implies\:Semi\:-\:perimeter\:=\:84\:cm}$

.°. The semi - perimeter is 84 cm.

Step2: Now to calculate the triangle area, we will again use the formula and substitute the values. [ Area of triangle = √s ( s - a ) ( s -b ) ( s - c )]

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

$\qquad\tt{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{84\:(\:\:84\:-\:56)\:(\:84\:-\:60\:)\:(\:84\:-\:52\:)} }$

$\qquad\tt{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{84\:(\:28\:)\:(\:24\:)\:(\:32\:)} }$

$\qquad\tt{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{84\:\times\:28\:\times\:24\:\times\:32\:} }$

$\qquad\tt{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{18,06,336}}$

$\qquad\tt{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:1344\:cm^{2}}$

.°. The area of the triangle is 1344 cm².

★ Answer:-      

• The area of the triangle is 1344 cm².