a We are given that the Heron's Formula relates the lengths of a triangle to the area of the triangle.
A=sqrt(s(s-a)(s-b)(s-c))In this formula a, b, and c are side lengths and s is the semiperimeter — half of the perimeter of this triangle. In our exercise we are asked to use this formula to find the area of a triangle with side lengths 7, 10, and 4. First let's evaluate the semiperimeter s.
The area of this triangle is approximately 10.9 square units.
b In this part we are asked to show that the areas found for a 5- 12- 13 right triangle are the same using Heron's formula and the standard area formula. First we will evaluate the semiperimeter of this triangle.
The semiperimeter is 15. Now we will substitute side lengths and the semiperimeter into the Heron's formula and check if the result is the same as using the standard formula. Notice that in a right triangle one leg is a base and the other is a height.
