Worksheets · Geometry

Rhombuses and kites worksheet

In a rhombus the diagonals meet at right angles and cut each other in half, so each quarter of the shape is a right triangle with half of each diagonal for legs. That is why the side comes from Pythagoras and the area is half the product. A kite's diagonals also meet at right angles, but only one of them is cut in half, and only one pair of opposite angles is equal.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

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Name

Rhombuses and Kites

Date Period

Find each measure.

  1. Find the area from the diagonals

    Find the area.1024
  2. Find the area.36160
  3. Find the area.50120

  1. Find the side from the diagonals

    Find the side.8084
  2. Find the side.4096
  3. Find the side.1824

  1. Find the other diagonal

    The side is 102. Find the other diagonal.96x
  2. The side is 20. Find the other diagonal.24x
  3. The side is 34. Find the other diagonal.32x

  1. Find angles in a kite

    Quadrilateral ABCD is a kite. Find x.A93°BCxD105°
  2. The figure is a kite. Find m∠B.AB(x + 94)°CD(3x + 68)°
  3. The figure is a kite. Find x.A59°B(x + 95)°CD(2x + 82)°

  1. Find kite sides from the diagonals

    The diagonals of kite ABCD meet at E, with AE=21, EC=15 and BE=DE=20. Find the length of its shorter side.ABCDE
  2. In kite ABCD the diagonals cross at E, and EC=15, AE=6 and BE=DE=8. Find CD.ABCDE

  1. Find rhombus angles using the diagonals

    In rhombus ABCD the diagonals meet at E, and m∠BAC=70∘. Find m∠BCD.
  2. In rhombus ABCD the diagonals meet at E, and m∠BAC=26∘. Find m∠BAD.

  1. Find angles and lengths in a kite

    ABCD is a kite. Find m∠ABE.ABCD47°E
  2. ABCD is a kite. Find BD.ABCDE5x − 463x − 26

  1. Find lengths and angles in a rhombus

    ABCD is a rhombus. Find x.ABCD6x − 49x + 21E
  2. ABCD is a rhombus. Find AC.ABCD17E

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Rhombuses and KitesAnswer keyVersion 1

Date Period

Find each measure.

  1. Find the area from the diagonals

    Find the area.1024120
  2. Find the area.361602880
  3. Find the area.501203000

  1. Find the side from the diagonals

    Find the side.808458
  2. Find the side.409652
  3. Find the side.182415

  1. Find the other diagonal

    The side is 102. Find the other diagonal.96x180
  2. The side is 20. Find the other diagonal.24x32
  3. The side is 34. Find the other diagonal.32x60

  1. Find angles in a kite

    Quadrilateral ABCD is a kite. Find x.A93°BCxD105°57∘
  2. The figure is a kite. Find m∠B.AB(x + 94)°CD(3x + 68)°107∘
  3. The figure is a kite. Find x.A59°B(x + 95)°CD(2x + 82)°13

  1. Find kite sides from the diagonals

    The diagonals of kite ABCD meet at E, with AE=21, EC=15 and BE=DE=20. Find the length of its shorter side.ABCDE25
  2. In kite ABCD the diagonals cross at E, and EC=15, AE=6 and BE=DE=8. Find CD.ABCDE17

  1. Find rhombus angles using the diagonals

    In rhombus ABCD the diagonals meet at E, and m∠BAC=70∘. Find m∠BCD.140∘
  2. In rhombus ABCD the diagonals meet at E, and m∠BAC=26∘. Find m∠BAD.52∘

  1. Find angles and lengths in a kite

    ABCD is a kite. Find m∠ABE.ABCD47°E43∘
  2. ABCD is a kite. Find BD.ABCDE5x − 463x − 268

  1. Find lengths and angles in a rhombus

    ABCD is a rhombus. Find x.ABCD6x − 49x + 21E14
  2. ABCD is a rhombus. Find AC.ABCD17E34

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Diagonals of 6 and 8

  1. Half of each is 3 and 4.
  2. Those are the legs of a right triangle.
  3. So the side is 5.

The answer is 5.

Where students go wrong

Using the whole diagonals as the legs. They bisect each other, so only half of each meets at the corner, and using both in full doubles the side.

Also called diagonals of a rhombus or kite properties.

What you can put on this worksheet

Area from the diagonals
Find the area. — a rhombus with diagonals 30 and 72 → 1080
The side from the diagonals
Find the side. — a rhombus with diagonals 30 and 72 → 39
The other diagonal
The side is 39. Find the other diagonal. — a rhombus with diagonals 30 and x → 72
Kites: angles
Quadrilateral ABCD is a kite. Find x. — a kite abcd with its angles marked, labeled A, 69°, B, C, D, 97° → 97∘
Kites: sides from the diagonals
The diagonals of kite ABCD meet at E, with EC=6, AE=15 and BE=DE=8. Find the length of its longer side. → 17
Rhombus angles from the diagonals
In rhombus ABCD the diagonals meet at E, and m∠BAC=44∘. Find m∠AEB. → 90∘
Kites with their diagonals
ABCD is a kite. Find BD. — a quadrilateral abcd with its diagonals meeting at e, labeled A, B, C, D, 16, E → 32
Rhombuses with their diagonals
ABCD is a rhombus. Find m∠BCD. — a quadrilateral abcd with its diagonals meeting at e, labeled A, B, C, D, 116°, E → 116∘
A rhombus corner from its diagonals, to a tenth
ABCD is a rhombus with AC=14 and BD=6. Find m∠ABC to the nearest tenth of a degree. — a quadrilateral abcd with its diagonals meeting at e, labeled A, B, C, D, E → 133.6∘

Questions about these worksheets

Yes. Every rhombuses and kites 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 rhombuses and kites 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 three 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 9: area from the diagonals, the side from the diagonals, the other diagonal, kites: angles, kites: sides from the diagonals, rhombus angles from the diagonals, kites with their diagonals, rhombuses with their diagonals and a rhombus corner from its diagonals, to a tenth. Tick as many as you want and set how many of each, or let it spread them evenly.

Using the whole diagonals as the legs. They bisect each other, so only half of each meets at the corner, and using both in full doubles the side.