ForHosting KIT · Math

Isosceles trapezoid calculator

Enter the two bases and the height of an isosceles trapezoid and get the whole figure: bases of 10 and 6 with a height of 4 give an area of 32, legs of 4.472136, diagonals of 8.944272 and base angles of 63.434949°. Free in your browser.

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Worked example

If you enter

Base a: 10
Base b: 6
Height: 4
Decimal places: 6

You get

Leg: 4.472136
Area: 32
Diagonal: 8.944272
Perimeter: 24.944272

Area, height, diagonals and angles of isosceles trapezoid. Search intent: isosceles trapezoid area. No network calls or random seeds are required. Failed jobs are not billed.

How three measurements fix the whole shape

An isosceles trapezoid has two parallel bases of different lengths and two equal slanted legs. Because the legs match, the long base sticks out by the same amount at each end: half the difference between the bases. That overhang and the height form a right triangle whose hypotenuse is the leg, so Pythagoras gives its length. From there, the perimeter is both bases plus twice the leg, the diagonal is the hypotenuse of another right triangle built on the height and on the long base minus one overhang, and the angles come from that same triangle. With bases of 10 and 6 and a height of 4, the overhang is 2, the leg 4.472136, the diagonal 8.944272 and the perimeter 24.944272.

Common trapezoid mistakes

The most frequent one is using the slanted leg as the height. The leg is always longer than the height, 4.472136 against 4 in the example, so the area comes out too large. The height is the perpendicular distance between the two bases. Another slip is swapping the bases: enter the longer one as the first base and the shorter one as the second. Finally, rounding intermediate values by hand shifts the last digits; the calculator rounds only once, at the end, to the number of decimals you choose.

What you can do with it

Teaching

Pinned goldens.

FAQ

How do I calculate the area of an isosceles trapezoid?

Add the two parallel bases, divide by two and multiply by the height. With bases of 10 and 6 and a height of 4, the mean base is 8 and the area is 32.

How do I find the length of the equal legs?

Each leg is the hypotenuse of a right triangle formed by the height and the overhang, the part of the long base that sticks out past the short one on each side. With bases of 10 and 6 the overhang is 2, so with a height of 4 the leg is 4.472136.

Are both diagonals of an isosceles trapezoid equal?

Yes. In an isosceles trapezoid the two diagonals always have the same length, which is why the result shows a single value: 8.944272 for bases of 10 and 6 and a height of 4.

Which angles does the calculator give?

The angle at each end of the long base, 63.434949° in the example with bases of 10 and 6 and a height of 4, and the angle at each end of the short base, 116.565051°. The two angles along one leg together make a straight angle.

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

POSThttps://api.kit.forhosting.com/math/isosceles-trapezoid

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/isosceles-trapezoid \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"base_a":10,"base_b":6,"leg":5}'

const res = await fetch("https://api.kit.forhosting.com/math/isosceles-trapezoid", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "base_a": 10,
    "base_b": 6,
    "leg": 5
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/math/isosceles-trapezoid",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "base_a": 10,
    "base_b": 6,
    "leg": 5
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/isosceles-trapezoid", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"base_a":10,"base_b":6,"leg":5}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"base_a":10,"base_b":6,"leg":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/isosceles-trapezoid", 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_a": 10,
  "base_b": 6,
  "leg": 5
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "math.isosceles_trapezoid",
  "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.

Technical notes

The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching demos.

How it works

Area, height, diagonals and angles of isosceles trapezoid. Area=(a+b)/2×h; leg/height related by Pythagoras on overhang. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching demos.

Inputs, limits and rounding

Optional decimals use half-up once. Optional output fields are omitted, never null. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Provide required JSON fields with DOM-safe names. Invalid types raise invalid_input. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks,

When to use it

Use when search intent matches. Area, height, diagonals and angles of isosceles trapezoid. EN-only delivery; Nitro hydrates locales. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching demos.

Integration use cases

Quick check

Free widget.

Automation

API same JSON.

Technical questions

Free?

Yes tier A.

Network?

No.

Bad input?

invalid_input.

API?

Yes.

Locales?

EN-only; Nitro hydrates.

Read the full KIT documentation →

Run — free