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Right Triangles by Area

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 33 of 60.

A right triangle's area is half the product of its two legs, the sides that meet at the right angle. With legs along the grid that is easy: legs 4 and 3 give area 6. Tilted legs work the same way.

$A right isosceles triangle with two legs of root 5$

Here AB is the step ⟨2, 1⟩ and AC is ⟨-1, 2⟩, the same step turned a quarter. So the angle at A is a right angle and both legs are √5. The triangle is right and isosceles, and its area is $\frac{1}{2}\cdot \sqrt{5}\cdot \sqrt{5} = \frac{5}{2}$ .

Challenge

On the squared paper, draw a right isosceles triangle with area 5: its two legs equal and at right angles. Then press Check.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Transformations & Constructions

1Translations

Sliding a Shape Draw the Image The Translation Rule Recap: Translations

4Combining Moves

One Move, Then Another Order Matters Two Mirrors Name the Move Recap: Combining Moves

7Drawing on Squared Paper

Lengths by Pythagoras Perpendicular Steps Squares by AreaRight Triangles by AreaMidpoints on the Grid Recap: Squared Paper

10Perpendiculars and Parallels

Perpendicular From a Point Perpendicular at a Point Parallel Through a Point Tools You Have Earned Recap: Parallels