Question

Use Heron's formula to find the area of the triangle with side lengths 9, 12, and 18, as shown below.

Answer 1

Answer: the answer is 48 or b

Explanation:

Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is given by:

A = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter, which is half the perimeter of the triangle:

s = (a + b + c) / 2

In this case, the side lengths are a = 9, b = 12, and c = 18. Therefore, the semiperimeter is:

s = (9 + 12 + 18) / 2 = 39 / 2

Using Heron's formula, we can now calculate the area of the triangle:

Answer 2

Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is:

A = sqrt(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by:

s = (a+b+c)/2

For the triangle with side lengths 9, 12, and 18, we have:

s = (9+12+18)/2 = 39/2

Using Heron's formula, we get:

A = sqrt((39/2)(39/2-9)(39/2-12)(39/2-18))

A = sqrt((39/2)(15/2)(27/2)(3/2))

A = sqrt(72915/16)

A ≈ 269.258

Therefore, the area of the triangle with side lengths 9, 12, and 18 is approximately 269.258 square units.