Question

Find the area of the triangle whose sides have the given lengths. (Round your answer to one decimal place.)

a = 7, b = 9, c = 11

Answer 1

The area of the triangle with sides 7, 9, and 11, calculated using Heron's formula, is approximately 34.96 square units.

Step-by-step explanation:

To find the area of a triangle with given side lengths of a = 7, b = 9, and c = 11, we can use Heron's formula, which is suitable for any triangle where the side lengths are known. First, we calculate the semi-perimeter, s, of the triangle using the formula s = (a + b + c) / 2. Then, we use Heron's formula which is Area = √(s(s - a)(s - b)(s - c)) to find the area.

Let's calculate the semi-perimeter:

s = (7 + 9 + 11) / 2
s = 27 / 2
s = 13.5

Now applying Heron's formula:

Area = √(13.5(13.5 - 7)(13.5 - 9)(13.5 - 11))
Area = √(13.5 × 6.5 × 4.5 × 2.5)
Area = √(1222.65625)
Area ≈ 34.96

Therefore, the area of the triangle is approximately 34.96 square units.