AI Geometry Solver
Geometry problems are mostly about picking the right formula and substituting carefully. This AI geometry solver names the formula, plugs in your measurements and keeps the units correct.
Common formulas the solver uses
| Shape | Area | Perimeter / surface |
|---|---|---|
| Rectangle | l × w | 2(l + w) |
| Triangle | ½ × base × height | Sum of the three sides |
| Circle | πr² | Circumference 2πr |
| Trapezium | ½(a + b)h | Sum of the four sides |
| Cylinder volume | πr²h | |
| Sphere volume | (4/3)πr³ | |
Describe the problem in words
Geometry is handled by the AI mode, so you can write the question naturally: Find the area of a triangle with base 10 cm and height 7 cm. Include every measurement and unit. If a diagram is involved, scan it with the math photo scanner or describe which sides and angles are given.
Units and common traps
Area is measured in square units (cm², m²) and volume in cubic units (cm³, m³). Always convert to the same unit before you start: mixing metres and centimetres is a frequent source of wrong answers. For right-angled triangles with missing sides or angles, the trigonometry solver covers the ratios in detail.
Worked examples
Example 1: Area of a triangle with base 10 cm and height 7 cm
- Use area = ½ × base × height.
- Substitute: ½ × 10 × 7 = 35.
Final answer: 35 cm²
Example 2: Circle with radius 6 cm: area and circumference
- Area = πr² = π × 36 = 36π ≈ 113.10 cm².
- Circumference = 2πr = 12π ≈ 37.70 cm.
Final answer: Area ≈ 113.10 cm²; circumference ≈ 37.70 cm
Example 3: Volume of a cylinder with radius 3 cm and height 10 cm
- Use V = πr²h.
- Substitute: π × 9 × 10 = 90π.
- Evaluate: 90π ≈ 282.74.
Final answer: ≈ 282.74 cm³
Example 4: Right triangle with legs 6 cm and 8 cm: find the hypotenuse
- Pythagoras: c² = 6² + 8² = 36 + 64 = 100.
- Take the square root: c = 10.
Final answer: 10 cm
Example 5: Two angles of a triangle are 50° and 65°. Find the third.
- Angles in a triangle sum to 180°.
- 180° − 50° − 65° = 65°.
Final answer: 65°
Common mistakes to avoid
- Using the diameter instead of the radius in circle formulas.
- Forgetting the ½ in the area of a triangle.
- Using the slanted side instead of the perpendicular height.
- Mixing units, for instance cm with m.
- Giving a volume in square units.
Frequently asked questions
What value of π does the solver use?
It keeps π exact where possible, such as 36π, and gives a decimal approximation using about 3.14159.
Can it solve 3D geometry?
Yes. Volume and surface area of prisms, cylinders, cones and spheres are supported through AI mode.
What if the diagram has no measurements?
The problem needs enough information to be solvable. List the given lengths and angles, and the solver will tell you what is missing.
Is coordinate geometry covered?
Yes. Distance between points, midpoints and equations of lines can be entered as written questions.
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AI-generated solutions are for learning purposes. Always verify important answers.