Free · Triangle calculators 🔺

Right Triangle Missing Measurements with Optional Area and Perimeter

Enter two legs, a leg and the hypotenuse, or a leg and area. Retain editable unit controls and optional area/perimeter measures, with positive right-triangle bounds.

  • Formula & worked example
  • Private in your browser
  • No signup
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Legs a=3 cm and b=4 cm give hypotenuse c=5 cm. When optional measures are shown, area is 6 cm² and perimeter is 12 cm.

a²+b² = c²; A = ab/2; P = a+b+c

Worked example

Enter these known values and leave the other values blank.

Right-angle leg a
3 cm
Right-angle leg b
4 cm
Optional area and perimeter
Show area and perimeter
Hypotenuse c
5 cm
Right-triangle area
6 cm²
Right-triangle perimeter
12 cm

Assumptions and limitations

  • a and b meet at a right angle; c is the hypotenuse. All sides, area and perimeter are positive. Unit selectors preserve their dimensions, and a supplied hypotenuse exceeds either known positive leg.
  • Show or hide the optional area/perimeter controls with the retained choice. Hiding them removes their public controls and results; the captured equations still compute their internal values.
  • Supported inverse pairs include both legs, either leg with the hypotenuse, and either leg with area. Area plus hypotenuse, perimeter plus hypotenuse, area plus perimeter or perimeter plus one leg alone does not recover both legs in these captured dependency rules.
  • The existing two-leg Pythagorean Theorem Calculator remains available with its acute-angle outputs. This additional workflow focuses on missing side measurements, units and optional area/perimeter; it does not add acute-angle fields to the source capture.
  • Use compatible units and clear unknowns before solving backward. Arithmetic has finite precision, and independently rounded measurements can be incompatible near a boundary.

Common questions

Which side is c?

c is the hypotenuse, opposite the right angle and longer than either positive leg. Entering a shorter value than a known leg is invalid.

Can I find a leg from area?

Yes, when the other leg is known: a = 2A/b or b = 2A/a. Enable the optional area/perimeter controls and leave the desired leg empty.

Does hiding the optional measures change the side formula?

No. It only hides the area/perimeter controls and result items. The Pythagorean side relationship remains a²+b²=c².

Where are the acute-angle results?

The existing two-leg Pythagorean Theorem Calculator provides acute angles. This source-based inverse workflow preserves its captured sides, optional area/perimeter and units without replacing that existing page.

References

Require a positive right triangle with a true hypotenuse and feasible optional area/perimeter measures; unsupported pairs remain incomplete rather than yielding fabricated legs. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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