测量计算器
Right Triangle Area from Inradius & Semiperimeter
Enter the inradius r and semiperimeter s to calculate the right triangle area.
通过半周长求面积 计算器
该计算器遵循 Area = r × s 并得出 Area。
输入数值以计算 Area。
Area
结果-
计算步骤
公式: Area = r × s
What This Calculator Solves
Calculate the total area of a right triangle when the inradius and semiperimeter are known.
This tool uses the elegant relationship between a triangle's inscribed circle and its semiperimeter to find the area instantly.
Known values
Inradius r and Semiperimeter s
Finds
Area (A)
Main formula
A = r × s
Best for
Advanced geometry and circle theorems
Area Formula
For any triangle, the area can be found by multiplying the inradius (r) by the semiperimeter (s).
This formula (A = r × s) is universally true for all triangles, not just right triangles.
Diagram: Inradius and Semiperimeter
The diagram illustrates the inscribed circle with radius r. The area of the full triangle is exactly r multiplied by the semiperimeter s.
Diagram Key
r = inradius
Radius of inscribed circle.
s = semiperimeter
Half the boundary distance.
A = area
Total enclosed space.
A = Area
Computed as r × s.
- Both r and s must be positive lengths.
How to Calculate
- Identify inradius r and semiperimeter s.
- Enter r into the first field.
- Enter s into the second field.
- Multiply them to get the Area.
Worked Example
If inradius is 2 and semiperimeter is 12 (as in a 6-8-10 triangle):
The area is 24 square units.
Where does this come from?
By splitting the triangle into three smaller triangles, each with height r and bases a, b, and c, their total area is 0.5*a*r + 0.5*b*r + 0.5*c*r = r*(a+b+c)/2 = r*s.
常见问题
关于直角三角形测量和面积的常见问题解答。
01 Does this work for non-right triangles? expand_more
Yes, A = rs works for any triangle.