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Area of an Oblique Triangle Calculator

Created by Aleksandra Zając, MD
Reviewed by Adena Benn
Last updated: Jan 18, 2024


Are you having a bunch of geometry tasks to solve? The area of an oblique triangle calculator is your buddy! Here, you can learn the area of oblique triangle formulas or just benefit from the fact that we've put all of them into a handy calculator for you.

What is an oblique triangle

An oblique triangle is a triangle that has no right angle (90°). In other words, any triangle that is not a right triangle is an oblique triangle.

Oblique triangles can be either acute or obtuse.

How to use the area of an oblique triangle calculator?

Using our oblique triangle area calculator is simple!

  1. First, choose the mode you want to work in. It depends on the data you already know - if those are sides, angles, height, etc.
  2. Depending on the mode, new rows will appear. Let's assume we choose the SAS (side-angle-side) mode.
  3. Input the length of the sides that you know. You can change the units at any time.
  4. Enter the value of the angle between the sides.
  5. The result appears immediately!
  6. If you want to change the mode, choose another one from the drop-down list—no need to restart the calculator.
  7. Now you know how to use the area of an oblique triangle calculator!

Tip: Check the next section if you're interested in the area of an oblique triangle formula that we use.

Calculating the area of an oblique triangle - formulas

There are four ways to find the area of an oblique triangle. The use depends on what data you have been given. You can calculate the area of an oblique triangle with sides and angles, with sides only, or with height and base.

Area of obtuse triangle formulas with known:

  1. Base (bb) and height (hh)
area=12×b×h\footnotesize\quad \text{area}=\frac{1}{2} \times b \times h
  1. Three sides (aa, bb, cc)
area=14×(a+b+c) ×(a+b+c)(ab+c) ×(a+bc)\footnotesize\quad \begin{align*} \text{area} &= \frac{1}{4} \times \sqrt{(a+b+c)}\ \times\\[1em] &\quad\sqrt{(-a+b+c)(a-b+c)}\ \times\\[1em] &\quad\sqrt{(a+b-c)} \end{align*}
  1. Two sides and the angle between them (sides – aa, bb; angle – γ\gamma)
area=12×a×b×sin(γ)\footnotesize\quad \text{area}=\frac{1}{2} \times a \times b \times \sin(\gamma)
  1. Two angles (γ\gamma, β\beta) and a side between them (aa)
area=a2×sin(β)×sin(γ)2×sin(β+γ)\footnotesize\quad \text{area} = a^2\! \times \sin(\beta)\! \times\! \frac{\sin(\gamma)}{2\! \times \sin(\beta + \gamma)}

FAQ

How do I calculate the area of an oblique triangle given 3 sides?

To calculate the area of oblique triangle given 3 sides, you need to use Heron's formula:
area = 0.25 × √[(a + b + c)(-a + b + c)(a - b + c)(a + b - c)]
.

How do I count the area of an oblique triangle given 3 sides?

Assuming the lengths of the sides are: 7, 8, and 13 inches, the area of this triangle is 24.25 in2.

Solution:

  1. Using Heron's formula:
    area = 0.25 × √[(a + b + c)(-a + b + c)(a - b + c)(a + b - c)]
  2. Knowing all three a, b, c (sides), solve the equation.
    area = 0.25 × √[(7 + 8 + 13)(-7 + 8 + 13)(7 - 8 + 13)(7 + 8 - 13)]
    = 0.25 × √[28 ×14 × 12 × 2]
    = 0.25 × √(9408)
    = 0.25 × 96.99
    = 24.25 in2

How do I calculate the area of an oblique triangle given the base and height?

Assuming the given base is 9 inches and the height 15 inches, the area of this triangle is 67.5 in2.

Step by step solution:

  1. Base (b) = 9 in, height (h) = 15 in.
  2. Formula for the area is (b × h)/ 2.
  3. Plugging in the numbers, you get:
    Area = (9 × 15)/2
    = 135/2
    = 67.5 in2
Aleksandra Zając, MD
Given
base and height
Triangle area: triangle with base and height





Base
in
Height
in
Area
in²
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