Right trapezoid area calculator
A right trapezoid with bases of 8 and 12 and a height of 5 has an area of 50: the average of the bases times the height. Enter the two parallel sides and the straight leg; the slanted side is never needed. Free in your browser.
- Free
- Runs in your browser
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- Your data stays on your device
Run — free
Worked example
- Base a
- 8
- Base b
- 12
- Height
- 5
- Area
- 50
A right trapezoid, also called a right-angled trapezoid or a right trapezium, is a quadrilateral with exactly one pair of parallel sides and two adjacent right angles. The parallel sides are the bases; the perpendicular distance between them is the height, and that height is also the length of the vertical leg. This calculator accepts the two base lengths and that perpendicular height, then returns the enclosed area. The closed-form identity is the average of the bases multiplied by the height, which is the same as splitting the figure into a rectangle plus a right triangle. There are no network calls, no random sampling, and no date dependence on the numbers you provide.
How a right trapezoid area is computed from two bases and height
A right trapezoid, also called a right-angled trapezoid in American usage and a right trapezium in British usage, is a four-sided polygon with exactly one pair of parallel sides and two adjacent interior angles of ninety degrees. The parallel sides are the bases; the non-parallel sides are the legs. Because two corners are right angles, one of those legs stands perpendicular to both bases and its length is exactly the height of the figure.
That is the geometric fact this calculator is built around: you never need the slanted leg, a diagonal, or an included angle in order to recover the area. Split the figure along a line from the shorter base down to the longer base, perpendicular to both. The split produces a rectangle whose width is the shorter base and whose height is the given height, plus a right triangle whose base is the difference of the two bases and whose height is the same perpendicular.
The rectangle area is the shorter base times the height. The triangle area is one-half the overhang times the height. Adding those two pieces yields the familiar closed form: the average of the two bases multiplied by the height.
Classic checks include bases eight and twelve with height five, which yield area fifty; bases ten and four with height six, which yield area forty-two; and a pair of equal bases, which collapses the triangle to zero overhang and leaves a rectangle. Swapping which base is labeled first does not change the area. Because the path uses only addition, subtraction, multiplication, and a single division by two, it is deterministic, constant time, and free of iterative solvers.
Where right trapezoid area calculations show up in real work
Secondary-school and college geometry courses constantly ask for the area of a right trapezoid given the two bases and the height, often next to a sketch that marks the two right angles and labels the vertical leg as h. That search is not the same as a general trapezoid landing: learners who type right trapezoid area want the two-right-angle figure, the vertical-leg-as-height fact, and the rectangle-plus-triangle picture, not a midsegment worksheet for an arbitrary trapezoid.
Construction, civil, and landscape workflows convert ramps, wing walls, retaining-wall elevations, and trapezoidal planting beds into area for material takeoffs; the same product feeds cost estimates once a unit price per square meter or square foot is applied downstream. Architecture and interior design tools review stepped floor plates, stadium seating sections, and right-angled terrace outlines as right trapezoids; area drives occupancy and material tables.
Game, graphics, and computer-aided design libraries store axis-aligned trapezoidal collision proxies and UI panels with one vertical side; deterministic area supports layout math and packing heuristics without a full computational-geometry stack. If you later need the slanted-leg length, the two diagonals, the perimeter of a general trapezoid, or unit conversion between square meters and square feet, treat those as separate search intents rather than overloading this right-trapezoid-area landing.
What you can do with it
Homework and exam checks
Compute right trapezoid area from two bases and height, and reject zero or negative dimensions with a clear error.
Ramps, walls, and material takeoffs
From measured bases and perpendicular height, recover area for retaining walls, ramps, and trapezoidal beds.
Layout and CAD proxies
Turn two parallel extents and a vertical height into area for panels, seating sections, and axis-aligned trapezoids.
FAQ
How do I find the area of a right trapezoid?
Send three positive finite numbers: the two parallel bases and the perpendicular height.
What makes a trapezoid a right trapezoid?
A right trapezoid has two adjacent right angles, so one non-parallel leg is perpendicular to both bases. That vertical leg is the height; you do not need the slanted leg to compute the area.
Why are zero and negative dimensions rejected?
A base or height that is not strictly positive is not a geometric side of a drawable right trapezoid.
Does the order of the two bases change the area?
Labeling is a convenience, not a geometric constraint.
Do I need the length of the slanted side?
No. In a right trapezoid one leg stands at right angles to both bases, so its length is the height. The two bases and that height are all the calculator needs to find the area.
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/right-trapezoid-area \
-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/right-trapezoid-area", {
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/right-trapezoid-area",
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/right-trapezoid-area", 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/right-trapezoid-area", 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.right_trapezoid_area",
"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
Students checking homework, carpenters sizing ramps and retaining walls, landscape designers laying trapezoidal beds, and graders that need a deterministic oracle all get the same pure result in the free browser tool and the API. Any base or height that is missing, not finite, or not strictly positive is rejected with invalid_input instead of a silent nonsense area.
How a right trapezoid area is computed from two bases and height
Huge magnitudes can still overflow IEEE-754 double range; when the sum overflows to a non-finite value the request fails with a clear message instead of returning Infinity in JSON. That closed form matches every elementary geometry textbook and keeps automated graders aligned with hand computation on the same three numbers. The response echoes both bases, the height, the computed area, and a short formula string so logs, worksheets, and teaching interfaces can document the algorithm without re-deriving it.
What you send and what you get back
The strictly positive gate is intentional: a zero base or a zero height would describe a degenerate segment or a collapsed figure, not a right trapezoid you can draw on a worksheet, so those inputs fail by name rather than returning a zero area that a buggy grader might treat as success. Example checks: bases eight and twelve with height five yield area fifty; bases three point five and six point five with height four yield area twenty; a height of zero or minus three fails naming the field. Wire the free browser tool for quick sanity checks, then call the identical contract from scripts for bulk evaluation without reimplementing the product in every language. Invalid input is not charged, so exploratory validation in continuous integration stays cheap while production calls remain predictable. Provide three required positive finite numbers: base_a is one parallel side, base_b is the other parallel side, and height is the perpendicular distance between those sides, which is also the length of the vertical right-angle leg. Missing fields, empty strings, non-numeric text, NaN, Infinity, zero, and any negative dimension 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 the average-of-bases identity so logs and teaching interfaces can document the algorithm. Numeric strings and integers are accepted the same way as JSON numbers. API pricing is the published base of $0.002 per successful item.
Where right trapezoid area calculations show 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.
Technical questions
What does the right 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.