Obtuse triangle area calculator
A base of 10 with a height of 4 gives an area of 20. Enter a base and its height, or the three sides, and from sides the calculator first proves the triangle is truly obtuse before giving its area. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Base
- 10
- Height
- 4
- Calculation mode
- base_height
- Area
- 20
When you send three sides, the capability first proves the triangle is valid and genuinely obtuse — one angle strictly greater than 90 degrees — and then applies Heron's formula. When you send a base and a height, it returns the classic half-base-times-height result. Any length that is not a positive number is rejected with a clear invalid-input error.
Two ways to describe the same triangle
Real problems hand you an obtuse triangle in one of two forms, and this capability speaks both. If you know the base and the perpendicular height — as in most school exercises, land measurements and CAD sketches — send those two numbers and you get the area directly as base times height divided by two.
If instead you know the three side lengths — as in surveying, truss design or any problem where the vertices are pinned by distances — send the three sides and the capability works out the area with Heron's formula. You never have to convert one description into the other yourself: there is no need to derive a height from three sides, and no need to invent sides when all you have is a height.
Why the obtuseness check matters
Three positive numbers do not automatically make a triangle, and a triangle is not automatically obtuse. Before any area is computed from sides, two tests run. Second, the obtuse test, which is just the converse of Pythagoras: only the angle opposite the longest side can exceed 90 degrees, so comparing the square of the longest side against the sum of the squares of the other two settles the whole triangle.
Validation, precision and determinism
Every length, whether it arrives as a base, a height or a side, must be a finite positive number. Zero, negative values, non-numeric strings and missing fields all produce the same clear invalid-input error naming the offending field, so calling code can surface the problem instead of guessing. The computation itself is elementary arithmetic plus one square root: no iteration, no approximation of angles, no trigonometric tables.
What you can do with it
Check homework and textbook exercises
Verify the area of an obtuse triangle given as base-and-height or as three sides, and see at a glance why an impossible set of sides is rejected.
Estimate land or material from surveyed sides
Turn three measured distances of an obtuse triangular plot or panel into square units without deriving heights by hand.
Gate a geometry pipeline
Reject inputs that are not obtuse triangles — bad sides, acute or right triangles — before area-dependent calculations run downstream.
FAQ
What inputs does it accept?
Either a base and its perpendicular height, or the three side lengths of the triangle.
What happens if a side is zero or negative?
Every length must be a positive finite number.
What if my three sides form an acute or right triangle?
The area is only returned for genuinely obtuse triangles.
How is the area from three sides calculated?
With Heron's formula, after the sides pass the triangle inequality and the obtuse test based on the converse of Pythagoras.
What units is the area in?
Square units matching your input: sides in metres give square metres, sides in inches give square inches. The capability is unit-agnostic.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/math/area-obtuse-triangle \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"base":10,"height":4}'const res = await fetch("https://api.kit.forhosting.com/math/area-obtuse-triangle", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"base": 10,
"height": 4
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/area-obtuse-triangle",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"base": 10,
"height": 4
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/area-obtuse-triangle", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"base":10,"height":4}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"base":10,"height":4}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/area-obtuse-triangle", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"base": 10,
"height": 4
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.area_obtuse_triangle",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
The obtuse triangle area API computes the area of an obtuse triangle in square units, accepting either of the two ways such a triangle is usually described: a base with its perpendicular height, or the three side lengths.
Two ways to describe the same triangle
Each request uses exactly one mode; mixing both in a single call is rejected so that contradictory inputs can never silently pick a winner.
Why the obtuseness check matters
First, the strict triangle inequality: the longest side must be shorter than the sum of the other two, otherwise the sides physically cannot close into a triangle and the request fails with a message that says so. If the triangle turns out to be acute or right, the request is rejected rather than returning a number that mislabels what you sent. This way the answer you get is never just an area — it is an area attached to a proof that your triangle is the kind you asked about.
Validation, precision and determinism
It runs free in your browser on this page with exactly the same code that serves the paid API, so the number you see while experimenting is the number your integration will receive at $0.002 per request.
Technical questions
What does it cost?
$0.002 per request. It is also free to run in your browser on this page, with the same code the API uses.