The formula this page uses
a² + b² = c² for a right triangle, and perimeter adds lengths while area multiplies two perpendicular ones
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AI Geometry Problem Solver
Solve ai geometry problem solver problems with clear steps, notation, and a final check.
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Evaluate the governing formula locally in your browser. Define each known quantity once, then change values to test another case instantly.
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Geometry
AI Geometry Problem Solver explained
The short version
- Most geometry word problems are easy once the sentence has been turned into a labelled sketch.
- Certain phrases always mean the same thing: 'leans against a wall' means a right angle, 'how much fencing' means perimeter.
- Draw it, label every known number with its unit, and mark the one thing you are being asked for.
What each part means
SymbolWhat it means
the sketch — Your diagramEven a rough one. It fixes which side is the hypotenuse before any arithmetic starts.
known lengths — Given measurementsWrite each one on the sketch with its unit, and convert so all units match.
the unknown — What is being askedMark it with a question mark so you do not solve for the wrong thing.
θ — An angleCheck whether the problem measures it from the ground, from a wall, or from north.
Show your work: a full example
- The problema 13 ft ladder leans against a wall with its foot 5 ft from the base; how high does it reach, and at what angle to the ground?
- Turn the words into a trianglethe wall is vertical and the ground horizontal, so the ladder is the hypotenuse, c = 13, and the 5 ft is the adjacent side
- Use Pythagoras13² − 5² = 169 − 25 = 144
- Square-root itheight = √144 = 12 ft
- For the angle, use the two sides you were givencos θ = 5/13 = 0.3846
- Inverse cosine in degree modeθ = 67.38°
- Check with a second ratiosin 67.38° = 0.9231, and 12/13 = 0.9231 ✓
A second, different case
- A different case: a composite shapea running track is a 84 m by 60 m rectangle with a semicircle on each short end; find the perimeter and the area
- Identify the piecestwo straights of 84 m, and two semicircles of diameter 60 m, so radius 30 m
- Two semicircles make one full circletheir curved edges total 2π(30) = 60π ≈ 188.50 m
- Perimeter2(84) + 188.50 = 168 + 188.50 = 356.50 m
- Area of the rectangle84 × 60 = 5040 m²
- Area of the two semicircles, again one full circleπ(30)² = 900π ≈ 2827.43 m²
- Total area5040 + 2827.43 = 7867.43 m²
Copy-ready example
a 13 ft ladder leans against a wall with its foot 5 ft from the base; how high does it reach, and at what angle to the ground?
The problem
Questions about the AI Geometry Problem Solver
How do I spot the hypotenuse from a description with no diagram?
It is the side opposite the right angle, and it is always the longest. A ladder, a rope, a ramp surface or a line of sight is usually the hypotenuse, while walls, ground and shadows are usually legs.
What should I draw first when the problem gives no picture?
Draw the ground as a horizontal line and anything vertical at a right angle to it. Then place the given numbers on the sides they belong to and put a question mark on the one you want. Half the errors disappear at that point.
Does an AI solver replace learning geometry?
No, and relying on it that way shows up in the next test. Use it to check a sketch and a final answer, and to see how a sentence maps onto a diagram, then redo the problem from your own drawing.
When should the answer stay exact rather than becoming a decimal?
Whenever π or a surd is involved and the question does not ask for a decimal. The track's area is exactly 5040 + 900π m², and 7867.43 is a rounded stand-in for it.