In Precalculus the area formulas sit with the Law of Sines and the Law of Cosines, for triangles with no right angle. When you have all three sides and no angle, Heron's formula gives the area directly.
Also taught in Geometry and Algebra 2, each at its own level and with its own examples.
Select your difficulty
Pick more than one for a sheet that mixes them.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
Using the full perimeter in Heron's formula. It needs half the perimeter, s, and the factors are s minus each side.
Also called area of a triangle with sine, one half ab sin C or included angle.
What you can put on this worksheet
Area from two sides and the angle between
Find the area — a triangle with sides 7 and 8 and an included angle of 90 degrees→ 28
Area with any angle, and Heron's formula
Two sides of a triangle are 9and 10, and the angle between them is 125∘. Find the area to the nearest tenth.→ 36.9
Regular polygons from the side or perimeter
Find the area of a regular octagon with side 9 in. Round to the nearest tenth.→ 391.1 in2
Area from one side and two angles
In triangle ABC, AB=36, m∠A=59∘and m∠B=69∘. Find the area to the nearest tenth.→ 658.1
Two sides and the angle between, drawn, any angle
Find the area to the nearest tenth — a triangle with two sides and the angle between them, labeled 92°, 16, 13→ 103.9
Questions about these worksheets
Yes. Every trigonometry and area sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the trigonometry and area questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 5: area from two sides and the angle between, area with any angle, and heron's formula, regular polygons from the side or perimeter, area from one side and two angles and two sides and the angle between, drawn, any angle. Tick as many as you want and set how many of each, or let it spread them evenly.
Using an angle that is not between the two sides. The formula needs the included angle; any other one belongs to a different triangle and gives the wrong area.