How do you use Heron's formula to find the area of a triangle with sides of lengths #14 #, #9 #, and #15 #?

Question

How do you use Heron's formula to find the area of a triangle with sides of lengths #14  #, #9    #, and #15   #?

Allison Allen · Accepted Answer

# Area=61.644# 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=14, b=9# and #c=15# #implies s=(14+9+15)/2=38/2=19# #implies s=19# #implies s-a=19-14=5, s-b=19-9=10 and s-c=19-15=4# #implies s-a=5, s-b=10 and s-c=4# #implies Area=sqrt(19*5*10*4)=sqrt3800=61.644# square units #implies Area=61.644# square units

Jayden Jackson · Answer

undefined To use Heron's formula to find the area of a triangle with sides of lengths 14, 9, and 15, follow these steps:

1. Calculate the semi-perimeter ($s$) of the triangle using the formula: $s = \frac{a + b + c}{2}$, where $a$, $b$, and $c$ are the lengths of the triangle's sides.
2. Use Heron's formula: $Area = \sqrt{s(s - a)(s - b)(s - c)}$, where $s$ is the semi-perimeter, and $a$, $b$, and $c$ are the lengths of the triangle's sides.
3. Substitute the values of $a$, $b$, and $c$ into the formula and calculate the area.

Given the sides of lengths 14, 9, and 15:

1. Calculate the semi-perimeter $s$:

$$s = \frac{14 + 9 + 15}{2} = \frac{38}{2} = 19$$

2. Use Heron's formula to find the area:

$$Area = \sqrt{19(19 - 14)(19 - 9)(19 - 15)}$$

$$Area = \sqrt{19 \times 5 \times 10 \times 4}$$

$$Area = \sqrt{3800}$$

$$Area \approx \sqrt{3800} \approx 61.639$$

So, the area of the triangle is approximately $61.639$ square units.