Area of an Obtuse Triangle Calculator
Calculate the area of obtuse triangles using various methods and formulas
Calculate Obtuse Triangle Area
Choose the method based on the information you have about the obtuse 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 10, 17, and 25 inches
Given: a = 10 in, b = 17 in, c = 25 in
Check validity: 10 + 17 > 25 ✓, 10 + 25 > 17 ✓, 17 + 25 > 10 ✓
Check if obtuse: 25² > 10² + 17² → 625 > 100 + 289 → 625 > 389 ✓
Semi-perimeter: s = (10 + 17 + 25) / 2 = 26 in
Step-by-Step Solution (Heron's Formula)
A = √[s(s-a)(s-b)(s-c)]
A = √[26 × (26-10) × (26-17) × (26-25)]
A = √[26 × 16 × 9 × 1]
A = √3744
A = 61.19 square inches
What is an Obtuse Triangle?
An obtuse triangle is a triangle with one interior angle greater than 90° (degrees). The side opposite to the obtuse angle is always the longest side of the triangle.
One angle > 90°: The obtuse angle
Two angles < 90°: Acute angles
Longest side: Opposite to obtuse angle
Types: Can be isosceles or scalene
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
Obtuse Triangle Properties
Sum of all angles equals 180°
One angle is greater than 90°
Longest side is opposite the obtuse angle
For sides a, b, c: c² > a² + b² (c is longest)
Cannot be equilateral
Understanding Obtuse Triangle Area Calculations
Identifying an Obtuse Triangle
An obtuse triangle is characterized by having one angle greater than 90°. This makes it different from acute triangles (all angles less than 90°) and right triangles (one angle exactly 90°). The obtuse angle is always opposite to the longest side.
Types of Obtuse Triangles
- •Obtuse Scalene: All sides are different lengths
- •Obtuse Isosceles: Two sides are equal (the obtuse angle is between the two equal sides)
Note: An obtuse triangle can never be equilateral since all angles in an equilateral triangle are 60°.
Formula Applications
Heron's Formula (SSS)
A = √[s(s-a)(s-b)(s-c)]
Where s = semi-perimeter = (a+b+c)/2
To verify obtuse: c² > a² + b² (c is longest side)
SAS Formula
A = (1/2) × a × b × sin(C)
Where C is the angle between sides a and b
For obtuse triangle: C > 90°
ASA Formula
A = (c² × sin(A) × sin(B)) / (2 × sin(C))
Where c is the side between angles A and B
One of A, B, or C must be > 90°
Real-World Applications
🏗️ Architecture & Construction
Calculate areas for sloped roofs, angled walls, and architectural features with obtuse angles.
📐 Engineering Design
Design structural elements, bridges, and mechanical parts with obtuse triangular sections.
🎨 Art & Design
Create artistic layouts, logos, and graphic designs incorporating obtuse triangular shapes.
🌍 Geographic Mapping
Calculate areas of irregular land plots and geographic features using triangulation.
🛠️ Manufacturing
Design and calculate material requirements for triangular components and parts.
🏡 Interior Design
Plan room layouts, furniture arrangements, and space utilization with obtuse triangular areas.