Area of an Oblique Triangle Calculator
Calculate the area of any oblique triangle using various methods and formulas
Calculate Oblique Triangle Area
Choose the method based on the information you have about the triangle
Length of the first side
Length of the second side
Length of the third side
Triangle Area Results
Example Calculation
Example: SSS Method with sides 7, 8, and 13 inches
Given: a = 7 in, b = 8 in, c = 13 in
Check validity: 7 + 8 > 13 ✓, 7 + 13 > 8 ✓, 8 + 13 > 7 ✓
Semi-perimeter: s = (7 + 8 + 13) / 2 = 14 in
Step-by-Step Solution (Heron's Formula)
A = √[s(s-a)(s-b)(s-c)]
A = √[14 × (14-7) × (14-8) × (14-13)]
A = √[14 × 7 × 6 × 1]
A = √588
A = 24.25 square inches
Calculation Methods
SSS - Three Sides
A = √[s(s-a)(s-b)(s-c)]
Use when you know all three side lengths
SAS - Two Sides + Angle
A = (1/2) × a × b × sin(C)
Use when you know two sides and the included angle
ASA - Two Angles + Side
A = (c² × sin(A) × sin(B)) / (2 × sin(C))
Use when you know two angles and the included side
Base and Height
A = (1/2) × base × height
Use when you know the base and perpendicular height
What is an Oblique Triangle?
An oblique triangle is any triangle that does not have a right angle (90°). This includes both acute triangles (all angles less than 90°) and obtuse triangles (one angle greater than 90°).
Acute Triangle: All angles < 90°
Obtuse Triangle: One angle > 90°
Triangle Tips
Sum of angles in any triangle equals 180°
Triangle inequality: sum of any two sides > third side
Larger angle is opposite to the longer side
Area formulas depend on known measurements
Understanding Oblique Triangle Area Calculations
What Makes a Triangle Oblique?
An oblique triangle is simply any triangle that doesn't have a right angle (90°). Unlike right triangles where we can easily use base × height ÷ 2, oblique triangles require different formulas depending on what measurements we know.
When to Use Each Method
- •SSS: When you know all three side lengths
- •SAS: When you know two sides and the angle between them
- •ASA: When you know two angles and the side between them
- •Base-Height: When you know the base and perpendicular height
Formula Explanations
Heron's Formula (SSS)
A = √[s(s-a)(s-b)(s-c)]
Where s = semi-perimeter = (a+b+c)/2
SAS Formula
A = (1/2) × a × b × sin(C)
Where C is the angle between sides a and b
ASA Formula
A = (c² × sin(A) × sin(B)) / (2 × sin(C))
Where c is the side between angles A and B
Real-World Applications
🏗️ Construction & Engineering
Calculate areas for irregular plots, roof sections, and structural elements in construction projects.
📐 Surveying & Mapping
Measure land areas using triangulation when direct measurement isn't possible.
⛵ Navigation & GPS
Calculate distances and areas using coordinate points and triangulation methods.
🎨 Design & Graphics
Calculate areas in graphic design, fabric cutting, and artistic layouts with irregular shapes.
🌍 Geography & Geology
Measure areas of geographical features, watersheds, and geological formations.
🏡 Real Estate & Property
Calculate property areas with irregular boundaries for accurate valuations.