Triangle Area: Sides 5, 5, 5
Calculate the area of a triangle with sides 5, 5, and 5 using Heron's formula.
Area:
Area = 10.825318 square units
Step-by-Step Solution
Step 1
Given Sides
a = 5
b = 5
c = 5
Step 2
Heron's Formula
Area = √[s(s-a)(s-b)(s-c)]
where s = (a + b + c) / 2
Step 3
Calculate Semi-perimeter
s = (a + b + c) / 2
s = (5 + 5 + 5) / 2
s = 7.5
Step 4
Calculate Factors
s - a = 7.5 - 5 = 2.5
s - b = 7.5 - 5 = 2.5
s - c = 7.5 - 5 = 2.5
Step 5
Calculate Product
s(s-a)(s-b)(s-c)
= 7.5 × 2.5 × 2.5 × 2.5
= 117.1875
Step 6
Calculate Area
Area = √117.1875
Area = 10.825318
Step 7
Additional Properties
Perimeter = 15
Inradius (r) = Area / s = 1.443376
Circumradius (R) = abc / (4·Area) = 2.886751
Step 8
Final Answer
Area = 10.825318
Heron's Formula
For a triangle with sides a, b, and c:
s = (a + b + c) / 2 (semi-perimeter)
Area = √[s(s-a)(s-b)(s-c)]
For this triangle: s = 7.5