Question

Find the area of a triangle whose sides are 4.5 cm and 10 cm and perimeter 10.5

Answer 1

Step-by-step explanation:

◾As we have given the two sides of triangle, let the three sides of triangle are (a) , (b), (c) .

◾And perimeter of given triangle is 10.5 cm

◾were, let us assume the sides are,

side a = 4.5 cm

side b = 10 cm

side c = ?

we know,

◾perimeter of triangle = sum of all sides of triangle

10.5 = side a + side b + side c

10.5 = 4.5 + 10 + side c

10.5 = 14.5 + side c

10.5 - 14.5 = side c

side c = 4 cm

[side be never in negative ]

therefor,

◾Now, we can use Hero's formula to find the area of triangle when sides of triangle are given.

◾Hero's formula

Hero's formula for area of triangle

= √[ s ( s - a ) ( s - b) (s - c) ]

◾For using this formula, we need to find the s (semiperimeter)

S = [side a + side b + side c ] / 2

= [ 4.5 + 10 + 4 ] / 2

= 9.25 cm

Therefor ,

◾Area of triangle abc = √[ s ( s - a ) ( s - b) (s - c) ]

= √[ 9.25 ( 9.25 - 4.5 ) ( 9.25 - 10 ) (9.25 - 4 ) ]

= √ [ 9.25 (( 4.75 ) ( -0.75 ) ( 5.25 ))]

=√ [( (9.25 ) (-3.5625) ( 5.25 ))

= √[ ((48.5625) ( (-3.5625)) ]

= √ [ 173 ( approximately) ]

= 13.15 ( approximately)

◾In the above, (-3.5625)) we taken as a (3.5625 ) because area is never as an imaginary .

◾here, we took a value (13.15) as an approx, up-to two decimals .

◾So, the area of a triangle whose sides are 4.5 cm and 10 cm and perimeter 10.5 [Area ]=

$\boxed{\textbf{\large{13.15cm square }}}$

Answer 2

13.15 sq

Step-by-step explanation:

let the third side be x then,

$4.5+10+x=10.5\\14.5+x=10.5\\14.5-10.5=x\\x=4$

area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

                             $s=\frac{4.5+10+4}{2}\\s=\frac{18.5}{2}\\s=9.25$

                              $\sqrt{9.25(9.25-4.5)(9.25-10)(9.5-4)} \\\sqrt{9.25\times4.75\times0.75\times5.25}$

                                =13.15 sq