Triangle Area: Sides 3, 4, 5
Calculate the area of a triangle with sides 3, 4, and 5 using Heron's formula.
Area:
Area = 6 square units
Step-by-Step Solution
Step 1
Given Sides
a = 3
b = 4
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 = (3 + 4 + 5) / 2
s = 6
Step 4
Calculate Factors
s - a = 6 - 3 = 3
s - b = 6 - 4 = 2
s - c = 6 - 5 = 1
Step 5
Calculate Product
s(s-a)(s-b)(s-c)
= 6 × 3 × 2 × 1
= 36
Step 6
Calculate Area
Area = √36
Area = 6
Step 7
Additional Properties
Perimeter = 12
Inradius (r) = Area / s = 1
Circumradius (R) = abc / (4·Area) = 2.5
Step 8
Final Answer
Area = 6
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 = 6