Free Area of an Obtuse Triangle Calculator

When working with triangles that contain an angle larger than 90°, the usual base‑height approach may not be enough. The Area of an Obtuse Triangle Calculator is a complete Obtuse Triangle Area tool that accepts several input formats—sides, angles, height and base—and instantly gives the correct area. Whether you are solving a geometry problem or measuring a real‑world shape, this Triangle Area Calculator adapts to your data and removes the need for manual number‑crunching.

What Makes a Triangle Obtuse?

An obtuse triangle has exactly one interior angle greater than $90^{\circ}$ (the obtuse angle); the other two angles are acute (less than $90^{\circ}$). Because the three angles must sum to $180^{\circ}$, the obtuse angle is always the largest angle in the triangle. Consequently, the side opposite this angle is the longest side. Obtuse triangles can be isosceles (two equal sides) or scalene (all sides different), but they can never be equilateral, because an equilateral triangle would have three angles of $60^{\circ}$.

How to Use the Calculator

The tool is designed around four common modes, and you choose the one that matches your data:

• Base and Height (B&H) – you know the length of one side (the base) and the perpendicular distance from that base to the opposite vertex.
• Side‑Angle‑Side (SAS) – you know two side lengths and the angle that is enclosed between them.
• Side‑Side‑Side (SSS) – you know all three side lengths.
• Angle‑Side‑Angle (ASA) – you know two angles and the side that lies between them.

After selecting the appropriate radio button, enter your numbers (the calculator lets you switch units at any time). The area result appears immediately in the output field. If you later want to try a different mode, just pick another option—no need to refresh or restart.

Area Formulas Used by the Calculator

Depending on the mode you select, the Obtuse Triangle Area tool applies one of the following well‑known formulas.

Base and Height

If you have the base length $b$ and the perpendicular height $h$:

$$\text{Area} = \frac{1}{2} \times b \times h$$

Three Sides — Heron’s Formula

When all three sides ($a$, $b$, $c$) are known, the Heron’s Formula Calculator component inside the tool does the work:

$$s = \frac{a + b + c}{2}$$ $$\text{Area} = \sqrt{s \times (s - a) \times (s - b) \times (s - c)}$$

For example, a triangle with side lengths 10 in, 17 in, and 25 in has a semi‑perimeter $s = 26$ in, and the formula yields an area of approximately $61.19\ \text{in}^{2}$.

Two Sides and the Included Angle — SAS

For the Triangle SAS Area Calculator mode, the area is obtained from:

$$\text{Area} = \frac{1}{2} \times a \times b \times \sin(\gamma)$$

where $\gamma$ is the angle between sides $a$ and $b$. Important: the angle must be the one that is actually between the two given sides; otherwise this formula does not apply.

Two Angles and a Side — ASA

When you supply two angles ($\beta$ and $\gamma$) and the side $a$ that lies between them:

$$\text{Area} = \frac{a^{2} \times \sin(\beta) \times \sin(\gamma)}{2 \times \sin(\beta + \gamma)}$$

As an illustration, for angles $97^{\circ}$ and $34^{\circ}$ with a side length of 13 inches between them, the area works out to about $62.14\ \text{in}^{2}$.

Types of Obtuse Triangles

As mentioned, an obtuse triangle can be isosceles (two sides equal) or scalene (no sides equal). The calculator does not require you to classify the triangle—it works purely from the numbers you enter, so both types are handled automatically.

Summary

The Area of an Obtuse Triangle Calculator is a versatile, all‑in‑one Triangle Area Calculator that covers every common scenario: base‑height, three sides (Heron’s formula), side‑angle‑side, and angle‑side‑angle. By incorporating these proven formulas, it serves as both a general Triangle Area Calculator and a specialized Obtuse Triangle Calculator for students, professionals, and anyone who needs fast, accurate area results.