Given , , and , use Heron's Area Formula to find the area of triangle . Round answer to two decimal places.
A) sq. units
B) sq. units
C) sq. units
D) sq. units
E) sq. units

Question

Given  ,  , and  , use Heron's Area Formula to find the area of triangle  . Round answer to two decimal places.
A) sq. units 
B) sq. units 
C) sq. units 
D) sq. units 
E) sq. units

Quizplus · Accepted Answer

Using Heron's Formula, we need to first find the lengths of the three sides of the triangle:

Side 1: Distance between (fd59_251e) and (fd59_251f)
= sqrt((251f - 251e)^2 + (acfc - acfc)^2 + (11ec1854 - 11ec1854)^2)
= sqrt(1^2 + 0^2 + 0^2)
= 1

Side 2: Distance between (fd58_fe0d) and (fd59_251f)
= sqrt((251f - fe0d)^2 + (acfc - acfc)^2 + (11ec1854 - 11ec1854)^2)
= sqrt(251f - fe0d)^2)
= sqrt(251f - 251e - 1)
= sqrt(0 + 1 + 1 + ... (50 times) ... + 1)
= sqrt(50)
= 5*sqrt(2)

Side 3: Distance between (fd58_fe0d) and (fd59_251e)
= sqrt((251e - fe0d)^2 + (acfc - acfc)^2 + (11ec1854 - 11ec1854)^2)
= sqrt(251e - fe0d)^2)
= sqrt(2520 - 251e - (251f - 251e) - 1)
= sqrt(20)
= 2*sqrt(5)

Now we can apply Heron's Formula to find the area:

s = (1/2)(1 + 5*sqrt(2) + 2*sqrt(5))
= 1 + (5/2)*sqrt(2) + sqrt(5)
Area = sqrt(s(s-1)(s-5*sqrt(2))(s-2*sqrt(5)))
= sqrt((61/4)*sqrt(2)*sqrt(5))
≈ 6.14

Rounded to two decimal places, the answer is 11ec1854_fd59_2524_acfc_c942729e9e87_TBX8702_11 sq. units.

Given , , and , Use Heron's