ForHosting KIT · Developer Utilities

Oblique prism volume

An oblique prism has two congruent parallel bases connected by parallelogram faces that are not necessarily perpendicular to the bases.

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The solid may lean, yet its volume is still the product of the base area and the perpendicular distance between those bases. Cavalieri's principle makes this precise: if every plane parallel to a fixed reference cuts two solids in regions of equal area, the solids have equal volume. An oblique prism and a right prism that share the same base area and the same orthogonal height therefore share the same volume formula V equals B times h. Students meet this result when a textbook shows a slanted figure and asks for volume without expanding every lateral edge. Architects, packaging designers, and CAD helpers need the same number when a drawing lists base area and story height rather than a full mesh. This capacity accepts strictly positive base_area and height, rejects zero or negative measures, and returns volume with the Cavalieri method tag as structured JSON. The same pure function powers the free browser widget and the prepaid API path, so a golden server example matches what a visitor runs locally with no network round trip and no language-model involvement.

How to use it

Enter your values in the form above. The tool checks them before calculating and shows the result on the same page.

Check your inputs

Use the labels and units shown next to each field. If something is missing or outside the allowed range, the page points to the field to fix.

Use it again or automate it

Use the browser tool for individual checks and the API when you need the same capability in an automated workflow.

What you can do with it

Get an answer now

Enter one set of values and see the result without building a spreadsheet or script.

Compare scenarios

Change one value at a time and rerun the calculation to understand what affects the result.

Automate repeated work

Use the API when the same calculation needs to run inside your product or workflow.

FAQ

How do I use this capability?

Complete the fields above and run it on this page. The form highlights anything that needs attention.

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

POSThttps://api.kit.forhosting.com/geom/oblique-prism

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/geom/oblique-prism \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"base_area":12,"height":5}'

const res = await fetch("https://api.kit.forhosting.com/geom/oblique-prism", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "base_area": 12,
    "height": 5
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/geom/oblique-prism",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "base_area": 12,
    "height": 5
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/oblique-prism", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"base_area":12,"height":5}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"base_area":12,"height":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/oblique-prism", 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_area": 12,
  "height": 5
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "geom.oblique_prism",
  "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

Per request$0.002

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.

Read the full KIT documentation →

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