Question

find the are of the triangles using heron's formula
1- 40cm,48cm,and22cm.
2-16cm,20cm,and22cm.

Answer 1

1)Given: a=40cm,b=48cm,c=22cm

  To Find: Area of triangle

  Solution: According to Heron's Formula, Area=$\sqrt{ s(s-a)(s-b)(s-c)$,

                  where s = semi-perimeter of triangle= $\frac{a+b+c}{2}$.

                   Here, s=$\frac{40+48+22}{2}$=55cm

              So, given measurements area=$\sqrt{55(55-40)(55-48)(55-22)}$ =436.549$cm^{2}$.

Hence, by Heron's formula, Area= 436.549$cm^{2}$.

1)Given: a=16cm,b=20cm,c=22cm

  To Find: Area of triangle

  Solution: According to Heron's Formula, Area=$\sqrt{ s(s-a)(s-b)(s-c)$,

                  where s = semi-perimeter of triangle= $\frac{a+b+c}{2}$.

                   Here, s=$\frac{16+20+22}{2}$=29cm

              So, given measurements area=$\sqrt{29(29-16)(29-20)(29-22)}$ =154.1134$cm^{2}$.

Hence, by Heron's formula, Area= 154.1134$cm^{2}$.

Answer 2

Answer:

Step-by-step explanation:

1) Given the lengths of side's are a= 40cm, b = 48cm and c = 22cm.

S = (a + b + c ) / 2 = (40 + 48 + 22) / 2 = 110 / 2 = 55cm

∴ A = √S (S-a)(S-b)(S-c)

= √55 (55-40)(55-48)(55-22)

= √55 (15)(7)(33)

= √190575

= 436.5 sq.cm.

2) Given the lengths of the side's are a= 16cm, b= 20cm and c= 22cm.

S = (a +b +c )/ 2 = (16+20+22)/ 2 = 58/2 = 29cm.

∴ A = √S (S -a)(S-b)(S-c)

= √29 (29-16)(29-20)(29-22)

= √29 (13)(9)(7)

= √23751

= 154.1 sq.cm.

[Area of a triangle for Heron's formula : A= √S (S -a )(S-b )(S-c ) ,where S= (a +b +c )/2]