Trigonometry and area worksheet for Geometry

Half the base times the height still works, but when you do not have the height you can use two sides and the angle between them instead. The sine of that angle supplies the height.

Also taught in Algebra 2 and Precalculus, each at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

Area of a Parallelogram (Geometry). Base times the perpendicular height.
Area of Triangles and Quadrilaterals (Geometry). The five formulas worth knowing.

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.



Sigma Prep · sigmaprep.io/worksheets Name Trigonometry and Area Date Period Find each area. Use the area formula $\frac{1}{2}ab\sin C$ What is the exact area of the triangle? Two sides of a triangle are $10$ and $12$ , and the angle between them is $85^{\circ}$ . Find the area to the nearest tenth. In $△ A B C$ , $A C = 8$ , $B C = 10$ and $m ∠ C = 30^{\circ}$ . Find the exact area. Find the area of $△ J K L$ if $J K = 7$ , $K L = 4$ and $m ∠ K = 99^{\circ}$ . Round to the nearest tenth. Find the exact area of the triangle. In $△ A B C$ , $a = 5$ , $b = 12$ and $m ∠ C = 132^{\circ}$ . Find the area to the nearest tenth. Find the exact area. Two straight fences, $9$ m and $5$ m long, meet at a $64^{\circ}$ angle, and a third closes off a triangular pen. What is its area, to the nearest tenth of a square meter? In $△ A B C$ , $B C = 3$ , $A B = 2$ and $m ∠ B = 150^{\circ}$ . Find the exact area. In $△ A B C$ , $a = 7$ , $c = 10$ and $m ∠ B = 23^{\circ}$ . Find the area to the nearest tenth. In $△ A B C$ , $m ∠ A = 135^{\circ}$ , $A B = 10$ and $A C = 4$ . Find the exact area of the triangle. Find the area of $△ P Q R$ if $P Q = 8$ , $P R = 14$ and $m ∠ P = 156^{\circ}$ . Round to the nearest tenth. What is the exact area of the triangle? Two straight fences, $10$ m and $5$ m long, meet at an $18^{\circ}$ angle, and a third closes off a triangular pen. What is its area, to the nearest tenth of a square meter? Find the area of a regular polygon Find the area of a regular pentagon with side 5 ft. Round to the nearest tenth. Find the area of a regular octagon with side 9 cm. Round to the nearest tenth. Find the area of a regular pentagon with side 9 in. Round to the nearest tenth. Find the area of a regular octagon with side 3 in. Round to the nearest tenth. Find the area of a regular octagon with side 15 ft. Round to the nearest tenth. Find the area of a regular octagon with side 8 m. Round to the nearest tenth. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Trigonometry and Area

Date Period

Find each area.

Use the area formula $\frac{1}{2}ab\sin C$
What is the exact area of the triangle?
Two sides of a triangle are $10$ and $12$ , and the angle between them is $85^{\circ}$ . Find the area to the nearest tenth.
In $△ A B C$ , $A C = 8$ , $B C = 10$ and $m ∠ C = 30^{\circ}$ . Find the exact area.
Find the area of $△ J K L$ if $J K = 7$ , $K L = 4$ and $m ∠ K = 99^{\circ}$ . Round to the nearest tenth.
Find the exact area of the triangle.
In $△ A B C$ , $a = 5$ , $b = 12$ and $m ∠ C = 132^{\circ}$ . Find the area to the nearest tenth.
Find the exact area.
Two straight fences, $9$ m and $5$ m long, meet at a $64^{\circ}$ angle, and a third closes off a triangular pen. What is its area, to the nearest tenth of a square meter?
In $△ A B C$ , $B C = 3$ , $A B = 2$ and $m ∠ B = 150^{\circ}$ . Find the exact area.
In $△ A B C$ , $a = 7$ , $c = 10$ and $m ∠ B = 23^{\circ}$ . Find the area to the nearest tenth.
In $△ A B C$ , $m ∠ A = 135^{\circ}$ , $A B = 10$ and $A C = 4$ . Find the exact area of the triangle.
Find the area of $△ P Q R$ if $P Q = 8$ , $P R = 14$ and $m ∠ P = 156^{\circ}$ . Round to the nearest tenth.
What is the exact area of the triangle?
Two straight fences, $10$ m and $5$ m long, meet at an $18^{\circ}$ angle, and a third closes off a triangular pen. What is its area, to the nearest tenth of a square meter?

Find the area of a regular polygon
Find the area of a regular pentagon with side 5 ft. Round to the nearest tenth.
Find the area of a regular octagon with side 9 cm. Round to the nearest tenth.
Find the area of a regular pentagon with side 9 in. Round to the nearest tenth.
Find the area of a regular octagon with side 3 in. Round to the nearest tenth.
Find the area of a regular octagon with side 15 ft. Round to the nearest tenth.
Find the area of a regular octagon with side 8 m. Round to the nearest tenth.



Sigma Prep · sigmaprep.io/worksheets Name Trigonometry and AreaAnswer keyVersion 1 Date Period Find each area. Use the area formula $\frac{1}{2}ab\sin C$ What is the exact area of the triangle? $3 \sqrt{2}$ Two sides of a triangle are $10$ and $12$ , and the angle between them is $85^{\circ}$ . Find the area to the nearest tenth. $59.8$ In $△ A B C$ , $A C = 8$ , $B C = 10$ and $m ∠ C = 30^{\circ}$ . Find the exact area. $20$ Find the area of $△ J K L$ if $J K = 7$ , $K L = 4$ and $m ∠ K = 99^{\circ}$ . Round to the nearest tenth. $13.8$ Find the exact area of the triangle. $\frac{45}{2}$ In $△ A B C$ , $a = 5$ , $b = 12$ and $m ∠ C = 132^{\circ}$ . Find the area to the nearest tenth. $22.3$ Find the exact area. $7 \sqrt{2}$ Two straight fences, $9$ m and $5$ m long, meet at a $64^{\circ}$ angle, and a third closes off a triangular pen. What is its area, to the nearest tenth of a square meter? $20.2$ In $△ A B C$ , $B C = 3$ , $A B = 2$ and $m ∠ B = 150^{\circ}$ . Find the exact area. $\frac{3}{2}$ In $△ A B C$ , $a = 7$ , $c = 10$ and $m ∠ B = 23^{\circ}$ . Find the area to the nearest tenth. $13.7$ In $△ A B C$ , $m ∠ A = 135^{\circ}$ , $A B = 10$ and $A C = 4$ . Find the exact area of the triangle. $10 \sqrt{2}$ Find the area of $△ P Q R$ if $P Q = 8$ , $P R = 14$ and $m ∠ P = 156^{\circ}$ . Round to the nearest tenth. $22.8$ What is the exact area of the triangle? $12$ Two straight fences, $10$ m and $5$ m long, meet at an $18^{\circ}$ angle, and a third closes off a triangular pen. What is its area, to the nearest tenth of a square meter? $7.7$ Find the area of a regular polygon Find the area of a regular pentagon with side 5 ft. Round to the nearest tenth. $43.0$ ft $^{2}$ Find the area of a regular octagon with side 9 cm. Round to the nearest tenth. $391.1$ cm $^{2}$ Find the area of a regular pentagon with side 9 in. Round to the nearest tenth. $139.4$ in $^{2}$ Find the area of a regular octagon with side 3 in. Round to the nearest tenth. $43.5$ in $^{2}$ Find the area of a regular octagon with side 15 ft. Round to the nearest tenth. $1086.4$ ft $^{2}$ Find the area of a regular octagon with side 8 m. Round to the nearest tenth. $309.0$ m $^{2}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Trigonometry and AreaAnswer keyVersion 1

Date Period

Find each area.

Use the area formula $\frac{1}{2}ab\sin C$
What is the exact area of the triangle? $3 \sqrt{2}$
Two sides of a triangle are $10$ and $12$ , and the angle between them is $85^{\circ}$ . Find the area to the nearest tenth. $59.8$
In $△ A B C$ , $A C = 8$ , $B C = 10$ and $m ∠ C = 30^{\circ}$ . Find the exact area. $20$
Find the area of $△ J K L$ if $J K = 7$ , $K L = 4$ and $m ∠ K = 99^{\circ}$ . Round to the nearest tenth. $13.8$
Find the exact area of the triangle. $\frac{45}{2}$
In $△ A B C$ , $a = 5$ , $b = 12$ and $m ∠ C = 132^{\circ}$ . Find the area to the nearest tenth. $22.3$
Find the exact area. $7 \sqrt{2}$
Two straight fences, $9$ m and $5$ m long, meet at a $64^{\circ}$ angle, and a third closes off a triangular pen. What is its area, to the nearest tenth of a square meter? $20.2$
In $△ A B C$ , $B C = 3$ , $A B = 2$ and $m ∠ B = 150^{\circ}$ . Find the exact area. $\frac{3}{2}$
In $△ A B C$ , $a = 7$ , $c = 10$ and $m ∠ B = 23^{\circ}$ . Find the area to the nearest tenth. $13.7$
In $△ A B C$ , $m ∠ A = 135^{\circ}$ , $A B = 10$ and $A C = 4$ . Find the exact area of the triangle. $10 \sqrt{2}$
Find the area of $△ P Q R$ if $P Q = 8$ , $P R = 14$ and $m ∠ P = 156^{\circ}$ . Round to the nearest tenth. $22.8$
What is the exact area of the triangle? $12$
Two straight fences, $10$ m and $5$ m long, meet at an $18^{\circ}$ angle, and a third closes off a triangular pen. What is its area, to the nearest tenth of a square meter? $7.7$

Find the area of a regular polygon
Find the area of a regular pentagon with side 5 ft. Round to the nearest tenth. $43.0$ ft $^{2}$
Find the area of a regular octagon with side 9 cm. Round to the nearest tenth. $391.1$ cm $^{2}$
Find the area of a regular pentagon with side 9 in. Round to the nearest tenth. $139.4$ in $^{2}$
Find the area of a regular octagon with side 3 in. Round to the nearest tenth. $43.5$ in $^{2}$
Find the area of a regular octagon with side 15 ft. Round to the nearest tenth. $1086.4$ ft $^{2}$
Find the area of a regular octagon with side 8 m. Round to the nearest tenth. $309.0$ m $^{2}$

How to do these

$a = 8, b = 5, C = 30^{\circ}$

Half of 8 times 5 is 20.
Sine of 30 is a half.
So the area is 10.

The answer is $10$ .

Where students go wrong

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.

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: In $△ A B C$ , $m ∠ B = 90^{\circ}$ , $B C = 7$ and $A B = 8$ . Find the exact area of the triangle. → $28$
Area with any angle, and Heron's formula: Two sides of a triangle are $9$ and $10$ , and the angle between them is $20^{\circ}$ . Find the area to the nearest tenth. → $15.4$
Regular polygons from the side or perimeter: Find the area of a regular octagon with side 9 in. Round to the nearest tenth. → $391.1$ in $^{2}$
Area from one side and two angles: In triangle $A B C$ , $A B = 36$ , $m ∠ A = 59^{\circ}$ and $m ∠ C = 52^{\circ}$ . Find the area to the nearest tenth. → $658.1$
Two sides and the angle between, drawn, any angle: Find the area of the triangle using $\frac{1}{2} a b \sin C$ , to the nearest tenth. — a triangle with two sides and the angle between them, labeled 95°, 8, 20 → $79.7$

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.

Geometry is usually taken around 9th or 10th 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.

Trigonometry and area worksheet for Geometry

Select your difficulty

Use the area formula 12absin⁡C\frac{1}{2}ab\sin C21​absinC

Find the area of a regular polygon

Use the area formula 12absin⁡C\frac{1}{2}ab\sin C21​absinC

Find the area of a regular polygon

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these trigonometry and area worksheets free?+

Do the trigonometry and area worksheets come with an answer key?+

Are these trigonometry and area worksheets printable?+

What grade are these trigonometry and area worksheets for?+

Can I get a different version of the same trigonometry and area worksheet?+

Is this a free alternative to Kuta Software for trigonometry and area?+

Can I choose how hard the trigonometry and area questions are?+

What kinds of question are on a trigonometry and area worksheet?+

What do students get wrong with trigonometry and area?+

Use the area formula $\frac{1}{2}ab\sin C$

Use the area formula $\frac{1}{2}ab\sin C$