2D Geometry Solver
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Result
Enter two points to find distance and midpoint.
Enter two points to find slope and line equation.
Find the point that divides P₁P₂ in the ratio m : n.
Enter two known angles to find the third.
Quick Examples
2D Geometry Solver: Area, Perimeter, Coordinates & Angles
Your complete guide to solving 2D geometry problems, from basic area and perimeter to coordinate geometry and polygon angles.
How to Use This 2D Geometry Solver
Pick a shape from the dropdown. Enter the dimensions you know and press Solve. The tool calculates area, perimeter, and diagonal (where applicable) with each step shown.
Example: Select Triangle, choose base and height mode, enter b = 8 and h = 5 to get area = 20 sq units instantly.
Choose Distance & Midpoint to find how far apart two points are and the point halfway between them. Use Slope & Line Equation to get the slope and full line equation. Use Section Formula to find a dividing point.
Example: Enter P(1, 2) and P(4, 6) to get distance = 5 and midpoint = (2.5, 4).
Find complementary or supplementary angles with one click. Enter two triangle angles to get the missing third. Enter the number of sides of a polygon to get every interior and exterior angle.
Example: Enter 6 sides to get hexagon interior angle = 120° and exterior angle = 60°.
2D Geometry Solver by Student Level
Topics: Area and perimeter of triangles, rectangles, squares, and parallelograms. Basic coordinate plotting. Identifying angle types.
How to use: Select the 2D Shapes tab and choose your shape. Enter the base and height given in your problem. Press Solve to see the formula and each multiplication step. Use this to check homework answers and learn where mistakes happen.
Tip: Always check your units. Area is always in square units (cm², m²) and perimeter is in regular units (cm, m).
Topics: Heron's formula, trapezoids, ellipses, regular polygons, coordinate geometry, distance formula, slope, midpoint, and angle sum theorems.
How to use: For GCSE, use Heron's formula for triangle problems where no height is given. Use the Coordinates tab for all graph-based questions. The Angles tab covers polygon theorems tested in IB and AP Pre-Calculus.
Tip: For IB and GCSE show-working questions, copy the step-by-step output from this solver into your written solution for full marks.
Topics: Coordinate geometry proofs, polygon properties, section formula, parametric curves, and ellipse equations in Calculus and Linear Algebra.
How to use: Use the Section Formula for problems involving ratio division of line segments. The Ellipse calculator helps verify area calculations used in integration problems. Polygon angle sums appear in combinatorics and graph theory.
Tip: The Ramanujan approximation for ellipse perimeter is accurate to within 0.002% for most axis ratios, making it reliable for engineering calculations.
Using This Solver for Geometry Assignments
Homework Problems
Work each problem by hand first, then use the solver to verify. Compare your answer to the step-by-step output line by line. The most common homework mistakes are using diameter instead of the correct formula input, forgetting to halve the base-height product for triangles, and confusing perimeter with area units.
Case Studies and Projects
Applied projects often ask you to find the area of a plot of land, the perimeter of a sports field, or the distance between two GPS coordinates. Enter the real measurements from your project into this geometry calculator and copy the step-by-step solution into your report to show your working clearly.
Quiz and Exam Practice
Click Random to get a random example. Solve it on paper in under 60 seconds, then check. Repeat 10 times before your test. Focus on the Coordinates tab since distance and midpoint problems appear on almost every GCSE and SAT geometry section.
Problem Sets
For multi-step problem sets, find the base dimensions first using the 2D Shapes tab, then switch to Coordinates for follow-up graph questions. Keeping the same measurements consistent across sub-parts is key to avoiding carry-through errors that cost marks on IB and AP exam papers.
What Is 2D Geometry?
What is a 2D shape in math?
A 2D shape is a flat figure that has only length and width. It has no depth. Common 2D shapes include triangles, rectangles, circles, trapezoids, and hexagons. Every 2D shape has an area (the space inside it) and a perimeter (the total distance around its edge).
What is the difference between area and perimeter?
Area measures how much surface a shape covers. It is always in square units such as cm² or m². Perimeter measures the total length of the boundary of a shape. It is in regular units like cm or m. A rectangle with length 10 and width 4 has area = 40 cm² and perimeter = 28 cm.
Triangle Area Calculator
How do you find the area of a triangle?
The most common formula is A = ½ × base × height. The height must be the perpendicular distance from the base to the opposite vertex. For a triangle with base 8 and height 5, area = ½ × 8 × 5 = 20 sq units. Select the Triangle shape in the 2D Shapes tab and choose Base & Height mode.
What is Heron's formula and when should I use it?
Use Heron's formula when you know all three side lengths but not the height. First find the semi-perimeter s = (a + b + c) / 2. Then area = √(s(s−a)(s−b)(s−c)). For sides 5, 6, 7: s = 9 and area = √(9 × 4 × 3 × 2) = √216 ≈ 14.70 sq units.
How do I solve a triangle area problem step by step?
Step 1: Identify what you are given (base and height, or three sides). Step 2: Choose the matching formula. Step 3: Substitute the values. Step 4: Calculate. Use the Three Sides (Heron's) mode in this solver to verify the result and see every step of the square root calculation shown clearly.
Real-world triangle area example
A triangular garden plot has a base of 12 m and a height of 9 m. How much turf is needed? Area = ½ × 12 × 9 = 54 m². Enter b = 12 and h = 9 in the Triangle solver to verify this instantly with full working shown.
Rectangle and Square Calculator
How do you calculate the area of a rectangle?
Area = length × width. For a rectangle with length 10 and width 6, area = 60 sq units. Perimeter = 2(l + w) = 2 × 16 = 32 units. The diagonal of a rectangle is d = √(l² + w²) = √(100 + 36) = √136 ≈ 11.66 units.
How do you find the diagonal of a square?
The diagonal of a square with side s is d = s√2. For s = 7, d = 7 × 1.4142 ≈ 9.90 units. The area is s² = 49 sq units and the perimeter is 4s = 28 units. The diagonal is longer than any side because it connects opposite corners.
Regular Polygon Calculator (Pentagon, Hexagon, Octagon)
How do I find the area of a regular hexagon?
For a regular hexagon with side s, area = (3√3 / 2) × s². For s = 5, area = (3 × 1.732 / 2) × 25 ≈ 64.95 sq units. Perimeter = 6s = 30 units. This solver uses the general regular polygon formula: A = (n × s²) / (4 tan(π/n)), which works for any regular polygon.
How do I calculate the area of a regular pentagon?
For a regular pentagon with side s, area = (s² / 4) × √(25 + 10√5). For s = 6, area ≈ 61.94 sq units. Perimeter = 5s = 30 units. Select Regular Pentagon from the dropdown and enter the side length to get the exact result with steps.
How do I find the area of a regular octagon?
For a regular octagon with side s, area = 2(1 + √2) × s². For s = 4, area = 2 × 2.4142 × 16 ≈ 77.25 sq units. Perimeter = 8s = 32 units. Regular octagons appear in road stop signs and architecture.
Trapezoid and Rhombus Calculator
How do you calculate the area of a trapezoid?
Area = ½ × (a + b) × h, where a and b are the two parallel sides and h is the perpendicular height between them. For a trapezoid with parallel sides 6 and 10, and height 4: area = ½ × 16 × 4 = 32 sq units. To get the perimeter, you also need both leg lengths.
How do you find the area of a rhombus?
Area = ½ × d&sub1; × d&sub2;, where d&sub1; and d&sub2; are the two diagonals. For diagonals 8 and 6, area = ½ × 8 × 6 = 24 sq units. The side length is √((d&sub1;/2)² + (d&sub2;/2)²) and the perimeter is four times the side length.
Coordinate Geometry Calculator
What is the distance formula in coordinate geometry?
The distance between two points (x&sub1;, y&sub1;) and (x&sub2;, y&sub2;) is d = √((x&sub2;−x&sub1;)² + (y&sub2;−y&sub1;)²). This comes directly from the Pythagorean theorem. For P(1, 2) and P(4, 6): d = √(9 + 16) = √25 = 5 units. Enter both points in the Distance & Midpoint operation to see every step.
How do I find the midpoint between two points?
The midpoint M = ((x&sub1;+x&sub2;)/2, (y&sub1;+y&sub2;)/2). For points (2, 4) and (8, 10), midpoint = (5, 7). The midpoint is always exactly halfway between the two points. This solver calculates the midpoint at the same time as the distance, so you get both results in one click.
How do I calculate the slope of a line through two points?
Slope m = (y&sub2;−y&sub1;) / (x&sub2;−x&sub1;). For P(1, 3) and P(4, 9): m = (9−3) / (4−1) = 6/3 = 2. The y-intercept is then c = y&sub1; − m×x&sub1; = 3 − 2 = 1. The full line equation is y = 2x + 1. A vertical line (x&sub1; = x&sub2;) has undefined slope.
What is the section formula and when do I use it?
The section formula finds the point P that divides the line segment from P&sub1; to P&sub2; in the ratio m:n. The formula is P = ((mx&sub2;+nx&sub1;)/(m+n), (my&sub2;+ny&sub1;)/(m+n)). If m = n, P is the midpoint. This formula is widely used in IB HL and A-Level coordinate geometry problems.
Angle Calculator
What are complementary and supplementary angles?
Complementary angles add up to 90°. If one angle is 35°, its complement is 55°. Supplementary angles add up to 180°. If one angle is 110°, its supplement is 70°. Use the Complementary & Supplementary option in the Angles tab to find either type instantly.
How do I find the missing angle in a triangle?
The three interior angles of any triangle always add up to 180°. If you know two angles A and B, then C = 180° − A − B. For A = 60° and B = 75°, C = 45°. Use the Triangle Missing Angle option in the Angles tab and enter the two known angles.
What is the interior angle sum of a polygon?
Sum of interior angles = (n−2) × 180°, where n is the number of sides. Triangle: 180°. Quadrilateral: 360°. Pentagon: 540°. Hexagon: 720°. Each interior angle of a regular polygon = (n−2) × 180° ÷ n. The exterior angle of each regular polygon = 360° ÷ n.
Explain exterior angles of a polygon
An exterior angle is formed by extending one side of a polygon at a vertex. For any convex polygon, the sum of all exterior angles is always exactly 360°. Each exterior angle of a regular polygon = 360° ÷ n. For a regular hexagon: each exterior angle = 60°. The interior and exterior angles at any vertex always add to 180°.
Real-World Uses of 2D Geometry
Where is 2D geometry used in real life?
Architects use rectangle and polygon area formulas to calculate floor plans. Farmers calculate field areas using triangles and trapezoids. Engineers use coordinate geometry to position components. Game developers use distance and slope formulas for collision detection and pathfinding.
How do architects use polygon geometry?
Architects calculate the area of every room using rectangle and polygon formulas. Hexagonal tiles and octagonal rooms require regular polygon area calculations. The coordinate geometry of a floor plan lets architects precisely place walls, doors, and windows using distance and slope calculations.
How is coordinate geometry used in navigation?
GPS systems use the distance formula to calculate how far apart two coordinates are. The midpoint formula helps find the center point of a route. Slope and line equations describe the direction of travel between two waypoints. Every digital map you use is built on these same coordinate geometry formulas.
Frequently Asked Questions
Need to solve 3D geometry? Try our 3D Geometry Calculator for volume and surface area of spheres, cylinders, cones, pyramids, and more.