How do you use Heron's formula to find the area of a triangle with sides of lengths #12 #, #8 #, and #11 #?

Question

How do you use Heron's formula to find the area of a triangle with sides of lengths #12  #, #8    #, and #11   #?

Violet Aldrich · Accepted Answer

#Area=42.7894# square units

Heron's formula for finding area of the triangle is given by #Area=sqrt(s(s-a)(s-b)(s-c))# Where #s# is the semi perimeter and is defined as #s=(a+b+c)/2# and #a, b, c# are the lengths of the three sides of the triangle. Here let #a=12, b=8# and #c=11# #implies s=(12+8+11)/2=31/2=15.5# #implies s=15.5# #implies s-a=15.5-12=3.5, s-b=15.5-8=7.5 and s-c=15.5-11=4.5# #implies s-a=3.5, s-b=7.5 and s-c=4.5# #implies Area=sqrt(15.5*3.5*7.5*4.5)=sqrt1830.9375=42.7894# square units #implies Area=42.7894# square units

Claire Akin · Answer

undefined To use Heron's formula to find the area of a triangle with sides of lengths 12, 8, and 11, we first need to calculate the semi-perimeter of the triangle. The semi-perimeter, denoted by 's', is found by adding the lengths of the three sides and dividing the sum by 2. In this case:

s = (12 + 8 + 11) / 2 = 31 / 2 = 15.5

Next, we use Heron's formula, which states that the area (A) of a triangle with sides of lengths a, b, and c, and semi-perimeter 's' is given by the formula:

A = √(s * (s - a) * (s - b) * (s - c))

Substituting the values we have:

A = √(15.5 * (15.5 - 12) * (15.5 - 8) * (15.5 - 11))

A = √(15.5 * 3.5 * 7.5 * 4.5)

A = √(185.625)

A ≈ 13.63 square units

Therefore, the area of the triangle with sides of lengths 12, 8, and 11 is approximately 13.63 square units.