Triangle Area: Sides 8, 15, 17
Calculate the area of a triangle with sides 8, 15, and 17 using Heron's formula.
Area:
Area = 60 square units
Step-by-Step Solution
Step 1
Given Sides
a = 8
b = 15
c = 17
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 = (8 + 15 + 17) / 2
s = 20
Step 4
Calculate Factors
s - a = 20 - 8 = 12
s - b = 20 - 15 = 5
s - c = 20 - 17 = 3
Step 5
Calculate Product
s(s-a)(s-b)(s-c)
= 20 × 12 × 5 × 3
= 3600
Step 6
Calculate Area
Area = √3600
Area = 60
Step 7
Additional Properties
Perimeter = 40
Inradius (r) = Area / s = 3
Circumradius (R) = abc / (4·Area) = 8.5
Step 8
Final Answer
Area = 60
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 = 20