How do you use Heron's formula to find the area of a triangle with sides of lengths #29 #, #25 #, and #12 #?

Question

How do you use Heron's formula to find the area of a triangle with sides of lengths #29  #, #25    #, and #12   #?

Avery Allen · Accepted Answer

Area of triangle is #148.92# If the sides of a triangle are #a#, #b# and #c#, then according to Heron's formula, the area of the triangle is given by the formula #Delta=sqrt(s(s-a)(s-b)(s-c))#, where #s=1/2(a+b+c)# Now given the sides of a triangle as #29#, #25# and #12# #s=1/2xx(29+25+12)=1/2xx66=33# and #Delta=sqrt(33(33-29)(33-25)(33-12))# = #sqrt(33xx4xx8xx21)# = #sqrt(3xx11xx2xx2xx2xx2xx2xx3xx7)# = #3xx2xx2sqrt(11xx2xx7)=12sqrt154=12xx12.41=148.92#

Parker Allen · Answer

undefined To use Heron's formula to find the area of a triangle with sides of lengths 29, 25, and 12, follow these steps:

1. Calculate the semi-perimeter (s) of the triangle:
s = (a + b + c) / 2, where a, b, and c are the lengths of the sides of the triangle.

2. Use Heron's formula to find the area (A) of the triangle:
A = sqrt(s * (s - a) * (s - b) * (s - c))

Substitute the values of the sides of the triangle into the formula:

a = 29, b = 25, c = 12

Calculate the semi-perimeter (s):

s = (29 + 25 + 12) / 2
s = 33

Now, substitute s and the side lengths into Heron's formula:

A = sqrt(33 * (33 - 29) * (33 - 25) * (33 - 12))
A = sqrt(33 * 4 * 8 * 21)
A = sqrt(5544)
A ≈ 74.5 square units

Therefore, the area of the triangle with sides of lengths 29, 25, and 12 is approximately 74.5 square units.