Home > Geometry > Heron's Formula

How do you use Heron's formula to find the area of a triangle with sides of lengths #23 #, #21 #, and #22 #?

Answer 1

Allison Allen

The Answer is 208.71 square units.

First we would find S which is the sum of the 3 sides divided by 2.

#S = (23 + 22 + 21)/2 # = #66/2# = 33

Then use Heron's Equation to calculate the area.

#Area = sqrt(S(S-A)(S-B)(S-C)) #

#Area = sqrt(33(33-23)(33-21)(33-22)) #

#Area = sqrt(33(10)(12)(11)) #

#Area = sqrt(43,560) #

#Area = 208.71 units^2 #

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Ella Armstrong

To use Heron's formula to find the area of a triangle with sides of lengths 23, 21, and 22, you first calculate the semi-perimeter (s) of the triangle by adding the lengths of all three sides and dividing by 2. Then, you use Heron's formula, which states that the area (A) of a triangle with side lengths a, b, and c and semi-perimeter s is given by the square root of s times (s-a) times (s-b) times (s-c). Substituting the given side lengths into the formula, you can calculate the area of the triangle.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.