Trapezoid area
A trapezoid with parallel sides of 8 and 12 and a height of 5 has an area of 50. Enter both bases and the perpendicular height and get the area as the average of the bases times the height. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Base a
- 8
- Base b
- 12
- Height
- 5
- Area
- 50
A trapezoid is a four-sided polygon with one pair of parallel sides, called the bases.
Where trapezoid area shows up in real work
Secondary-school and college geometry courses constantly ask students to find the area of a trapezoid when the two parallel bases and the height are given; a trusted calculator with a strict positive gate speeds homework grading and removes spreadsheet mistakes where someone multiplies all four side lengths or treats a slanted leg as the height. Architecture and interior workflows estimate material for trapezoid panels, roof sections, and parcel patches when the two parallel edges are measured on site and the clearance height is known from drawings.
Manufacturing and fabrication teams size trapezoid plates, hopper sides, and duct transitions; when the two parallel edges are fixed by mating parts and the height is fixed by clearance rules, area is the quantity that drives material cost and weight. Civil and landscape notes often record a roadside verge, a retaining-wall face, or a garden bed as a trapezoid with two parallel edges of different length; converting those three measurements into area is the step that feeds soil, paint, or cladding quantities.
Game, graphics, and CAD libraries store trapezoid quads for terrain skirts, UI panels, and UV shells; deterministic area from two bases and height supports layout math and collision proxies without a full computational-geometry stack. If you later need the diagonals of a trapezoid, the non-parallel legs, or a general quadrilateral area from four sides and an angle, treat those as separate search intents rather than overloading this trapezoid-area landing.
What you can do with it
Panels, plates, and site sketches
When two parallel edges and the perpendicular height are measured, compute the matching area for material, cut lists, and layout notes.
FAQ
Does height have to be perpendicular to the bases?
Yes. height is the perpendicular distance between the two parallel sides. A slanted non-parallel leg is not the height and will give the wrong area if you send it as height.
How do I calculate the area of a trapezoid?
Add the two parallel sides, divide by two and multiply by the perpendicular height. With bases of 8 and 12 and a height of 5, the average base is 10, so the area is 50.
What happens if a base or the height is zero or negative?
The calculation does not run. All three lengths must be greater than zero, because a zero or negative length does not describe a trapezoid you could draw, and a result built on it would be misleading.
Can I use lengths with decimals?
Yes. Any positive length works, decimals included. Bases of 5.5 and 10.5 with a height of 4, for example, give an area of 32, in the same square unit as your measurements.
Can this calculator find the diagonals or the slanted sides?
No. It works out the area from the two parallel sides and the height only. Diagonals, the non-parallel legs or the area of a general four-sided shape are separate calculations.
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/trapezoid \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"base_a":8,"base_b":12,"height":5}'const res = await fetch("https://api.kit.forhosting.com/math/trapezoid", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"base_a": 8,
"base_b": 12,
"height": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/trapezoid",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"base_a": 8,
"base_b": 12,
"height": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/trapezoid", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"base_a":8,"base_b":12,"height":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"base_a":8,"base_b":12,"height":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/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": 8,
"base_b": 12,
"height": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.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
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
Its enclosed area is the product of the perpendicular height and the average of those two bases: A equals (base_a plus base_b) divided by two, times height. This calculator accepts three strictly positive finite lengths, applies that closed-form identity, and returns the area as structured JSON so homework checks, site sketches, and fabrication notes stay aligned with the same arithmetic. Zero, negative, missing, and non-numeric values fail with invalid_input and are not billed. A successful API call costs $0.002.
How trapezoid area is computed from two bases and height
The height must be perpendicular to the bases you chose; using a non-parallel slanted side instead of the altitude overstates or understates the true area. Classic checks include bases eight and twelve with height five yielding area fifty; bases five and nine with height four yielding area twenty-eight; and bases five point five and ten point five with height four yielding area thirty-two. Because the path uses a single average-and-multiply after finite-number checks, it is deterministic, O(1), and free of iterative solvers. Label the two parallel sides as base_a and base_b, and measure the perpendicular distance between those parallels as the height. The standard area formula is the average of the bases times the height, written A = (base_a + base_b) / 2 × height. That identity is the same as saying the area equals the length of the midsegment times the height, because the midsegment is defined as the average of the two parallel sides. This engine adds the two validated bases, divides by two, multiplies by the validated height, and returns the product as the enclosed area. Huge magnitudes can still overflow IEEE-754 double range; when the product is non-finite the request fails with a clear overflow message instead of returning Infinity in JSON. That closed form matches analytic geometry textbooks and keeps automated graders aligned with hand computation on the same three numbers. The response echoes the inputs, the area, and the formula string so logs and teaching UIs can document the algorithm without reading the source.
What you send and what you get back
Zero is rejected as well as every negative, because a degenerate trapezoid with a vanished base or vanished height is not a positive-area figure under this contract. Example checks: bases eight and twelve with height five yield area fifty; bases six and ten with height three yield area twenty-four; height zero or height negative fails naming the height field. Wire the free browser tool for quick sanity checks, then call the identical contract from scripts for bulk evaluation without reimplementing the average-of-bases identity in every language. Provide three required finite numbers: base_a is the length of the first parallel side and must be strictly positive, base_b is the length of the second parallel side and must be strictly positive, and height is the perpendicular altitude between those parallels and must be strictly positive. Missing fields, empty strings, non-numeric text, NaN, Infinity, zero, and negative dimensions are rejected with invalid_input and are not charged. On success the JSON response returns base_a, base_b, height, area, and formula set to area = (base_a + base_b) / 2 × height so graders and pipelines can assert both the number and the algorithm. API pricing is the published base of $0.002 per successful item.
Where trapezoid area shows up in real work
Because this capability is a pure parse engine, failed validation does not consume balance and successful runs stay at $0.002 per item.
Integration use cases
Homework and exam checks
Compute enclosed trapezoid area from textbook bases and height, and reject a zero or negative dimension with a clear invalid_input error.
CAD and automated geometry fixtures
Turn two bases and a height into a reproducible area for tests, docs, and trapezoid assets in browser or API.
Technical questions
How do I compute the area of a trapezoid?
Send three positive finite numbers: base_a, base_b, and height. The API returns area = (base_a + base_b) / 2 × height together with the echoed inputs and the formula string.
What happens if a base or the height is zero or negative?
The task fails with invalid_input. This contract requires strictly positive finite lengths, so zero and negative dimensions are rejected and are not billed.
Which field names and aliases are accepted?
Canonical fields are base_a, base_b, and height. Aliases a, base1, or top map to base_a; b, base2, or bottom map to base_b; h or height_length map to height.
What does the trapezoid area calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.