Create a word problem of your own about a triangle in any sports field. Write measures
of all sides. Find area of the triangle by using Heron's
formula.
Sure! Here's a word problem about a triangle on a soccer field:
In a soccer field, there is a triangular area called the penalty area. Let's say one side of the penalty area is the goal line, which has a length of 10 meters. Another side is the 18-yard line, which measures 16 meters. The last side is the diagonal of the penalty area, which connects the corners of the goal line and the 18-yard line.
To find the area of the penalty area, we can use Heron's formula.
Heron's formula states that the area of a triangle can be found using the lengths of its sides. The formula is as follows:
Area = √(s(s-a)(s-b)(s-c))
Where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of the sides.
To find the semi-perimeter, we add all three sides and divide the sum by 2:
s = (10 + 16 + √(10^2 + 16^2))/2
s = (10 + 16 + √(100 + 256))/2
s = (10 + 16 + √356)/2
s = (26 + √356)/2
s ≈ 32.53
Now, we can substitute the values of s, a, b, and c into Heron's formula:
Area = √(32.53 * (32.53 - 10) * (32.53 - 16) * (32.53 - √(10^2 + 16^2)))
Area = √(32.53 * 22.53 * 16.53 * (32.53 - √356))
Area ≈ √(12089.99 * 368.025 * (32.53 - √356))
Area ≈ √(4493360.71 * (32.53 - √356))
Area ≈ √(146309451.27)
Area ≈ 12096.86 square meters
Therefore, the area of the penalty area on the soccer field is approximately 12096.86 square meters.