Math Problem Statement
Solution
The given formula represents Heron's formula for the area of a triangle when the lengths of its three sides , , and are known, along with the semi-perimeter :
The problem provides the following values:
- inches (which is inches),
- inches (which is inches),
- inches (which is inches),
- inches.
Step-by-step solution:
-
Subtract each side from the semi-perimeter:
-
Substitute all the values into the formula:
-
Calculate the product:
-
Take the square root:
Thus, the area of the triangle is approximately .
Would you like more details on any of the steps, or further clarifications?
Here are 5 related questions for further exploration:
- How would the area change if the semi-perimeter were different?
- What does the semi-perimeter represent geometrically?
- Can Heron’s formula be used for a right triangle, and how does it compare with the usual area formula for such triangles?
- What would the area be if the triangle were equilateral, with all sides equal?
- How do we handle a situation where the semi-perimeter is smaller than one of the sides?
Tip: When using Heron's formula, always ensure that the sum of any two sides is greater than the third, as required by the triangle inequality.
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Formulas
Heron's Formula: A = sqrt(s(s-a)(s-b)(s-c))
Theorems
Heron's Theorem
Suitable Grade Level
Grades 9-12
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