HexMathv1.0.3

Geometry calculator with steps

Type or scan a geometry problem. HexMath names the formula and works out the length, area or volume.

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What this page covers

  • Right triangles with the Pythagorean theorem.
  • Areas of triangles, trapezoids, circles and other polygons, and volumes and diagonals of boxes and other solids.
  • Distances between two points on a coordinate grid.
  • Not covered here: drawings and constructions, and proofs; for angles found with sine and cosine use the trig calculator.

How to enter the problem

  • Type it or paste it. Name the shape and give each measurement, for example right triangle, legs 7 and 24, find the hypotenuse.
  • Scan it. Fit the one problem in the frame.
  • Choose a photo. Several problems in one photo are solved as a list.
  • Then tap Solve.

Worked examples

Example 1

Problem

Find the area of a trapezoid with parallel sides 6\displaystyle 6 and 10\displaystyle 10 and height 5\displaystyle 5.

Answer

Verified

The answer is

A=40A = 40

Explanation

  1. Write the formula
    A=12(a+b)hA = \frac{1}{2}(a + b)h, the average of the parallel sides times the height.
  2. Add the parallel sides
    6+10=166 + 10 = 16, and half of that is 88.
  3. Multiply by the height
    A=8⋅5=40A = 8 \cdot 5 = 40 square units.

Example 2

Problem

Find the distance between the points (1,2)\displaystyle (1, 2) and (7,10)\displaystyle (7, 10).

Answer

Verified

The answer is

d=10d = 10

Explanation

  1. Find the changes
    Across: 7−1=67 - 1 = 6. Up
    10−2=810 - 2 = 8
  2. Use the distance formula
    d=62+82=36+64=100d = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100}
  3. Simplify
    d=10d = 10

Example 3

Problem

A box measures 3\displaystyle 3 by 4\displaystyle 4 by 12\displaystyle 12. Find the length of its longest diagonal, corner to opposite corner.

Answer

Verified

The answer is

1313

Explanation

  1. Find the diagonal of the base
    32+42=25=5\sqrt{3^2 + 4^2} = \sqrt{25} = 5
  2. Use the height
    The base diagonal and the height 1212 form a right triangle with the space diagonal as hypotenuse.
  3. Apply the Pythagorean theorem again
    52+122=169=13\sqrt{5^2 + 12^2} = \sqrt{169} = 13

Common mistakes

  • Adding the legs instead of their squares. Legs 7 and 24 give a hypotenuse of 2525, not 3131.
  • Forgetting the one half in the trapezoid formula, which doubles the area to 8080 instead of 4040.
  • Forgetting the square root in the distance formula, which gives 100100 instead of 1010.
  • Mixing units, such as a radius in centimetres and a height in metres.

Checks, assumptions and limits

  • Check by hand: the hypotenuse is the longest side, so it must be longer than each leg and shorter than their sum.
  • Answers are in the same unit as the measurements given; areas are in square units and volumes in cubic units.
  • HexMath can make mistakes. Double check important steps.

Related tasks

Frequently asked questions

Yes. Scan or choose a photo of the problem. Make sure the measurements are written clearly in the picture or the text.

Yes. Answers with square roots or pi are kept exact, such as the square root of 57. If you want a decimal, ask for one in the problem.

Each step names the formula it uses, such as the Pythagorean theorem or the area of a trapezoid, before putting in the numbers.

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Last updated: · HexMath