Rectangles, Rhombi and Squares
Special parallelograms with extra properties.
About this topic
A rectangle is a parallelogram with four right angles and equal diagonals. A rhombus has four equal sides and perpendicular diagonals that bisect its angles. A square has all the properties of both.
Area of a rectangle is length × width, of a rhombus is half the product of its diagonals, and of a square is side². Understanding which properties belong to which shape helps in proofs and classification.
Worked example: a rectangle has sides 6 and 8, so its diagonal is 10 and its area is 48. A rhombus with diagonals 10 and 24 has area ½ × 10 × 24 = 120, and by the Pythagorean theorem each side is √(5² + 12²) = 13. A square of side 5 has area 25 and diagonal 5√2.
These shapes are everywhere: screens, floor tiles, kite frames and diamond signs. A common misconception is that a rhombus has right angles or equal diagonals; only a square does. A rectangle does not have perpendicular diagonals unless it is a square. A good way to separate them is to ask what is equal: a rectangle has equal diagonals, a rhombus equal sides, and a square has both. Use the diagonal formula for the rhombus when sides are not given.
Key ideas
- Rectangle: four right angles, equal diagonals
- Rhombus: four equal sides, perpendicular diagonals
- Square: both
Quick check
Use cases: where Rectangles, Rhombi and Squares helps
- Homework: review the key idea behind Rectangles, Rhombi and Squares before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Rectangles, Rhombi and Squares without notes.
- Visual learning: play with the interactive lab to see how Rectangles, Rhombi and Squares changes when you adjust its inputs.
- Teaching a friend: explain Rectangles, Rhombi and Squares in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Rectangles, Rhombi and Squares?
Special parallelograms with extra properties.
What will I learn in Rectangles, Rhombi and Squares?
Rectangle: four right angles, equal diagonals. Rhombus: four equal sides, perpendicular diagonals. Square: both.
Is Rectangles, Rhombi and Squares part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Rectangles, Rhombi and Squares lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Rectangles, Rhombi and Squares?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.