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Geometry

Area of a triangle

Find a triangle area from base and height, or from three side lengths with Heron's formula.

Open in Trident

When you know the base b and the height h, the area is ½ × b × h. For b = 12 and h = 7 the area is 42.

When you only know the three sides a, b and c, use Heron's formula. First find s = (a + b + c) / 2, then area = √(s(s−a)(s−b)(s−c)). For sides 5, 6 and 7, s is 9 and the area is √216 = 14.697.

Natural Scientific 991 · Base and height

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

  1. Type 12 × 7 ÷ 2 and press =.

    12×7÷2=

You should see12×7÷2 42

Natural Scientific 991 key reference

RPN Scientific 15 · Base and height

Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.

  1. Key in 12 ENTER 7 and multiply. Key in 2 and divide.

    12ENTER7×2÷

You should see42.0000

RPN Scientific 15 key reference

Classic Graphing 84 · Heron's formula

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

  1. First work out s by hand: (5 + 6 + 7) / 2 = 9. Open the root with 2nd and x² and type 9 × (9 − 5) × (9 − 6) × (9 − 7).

    2nd√x²9×(9−5)×(9−6)×(9−7)

  2. Close the bracket and press enter.

    )enter

You should see√(9*(9−5)*(9−6)*(9−7)) 14.69693846

Classic Graphing 84 key reference

Classic CAS · Heron's formula

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

  1. Press ctrl and x² for the root and open a bracket. Type 9 × (9 − 5) × (9 − 6) × (9 − 7), close the bracket and press enter.

    ctrl√x²(9×(9−5)×(9−6)×(9−7))enter

You should see6·√6

The exact answer 6√6 is about 14.697.

Classic CAS key reference

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