The Equilateral Triangle
Part of the Triangles section of Coddy's Geometry journey. Lesson 56 of 63.
An equilateral triangle is isosceles from every side, so its height also lands on the midpoint of the base. The two halves are 30-60-90 triangles: the full side is the hypotenuse and half the side is the short leg.
With side 6, half the base is 3 and the height is √(6^2 - 3^2) = √(27) = 3×√(3), the long leg of the 30-60-90 triangle. The area is 1/2 × 6 × 3×√(3) = 9×√(3). Exact answers keep the √3.
On the stage there are several routes: the midpoint and Pythagoras, or the 60° angle and the special right triangle. Any route that names a true rule at each step is fine.
Challenge
△ABC is equilateral, all three sides ticked, with side BC = 10 and its height AD drawn. Find the exact area of △ABC, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Triangles
1Sides and Names
Three Sides, Three CornersSorting by SidesNaming by AnglesTicks into EquationsThe Longest SideRecap: Sorting Triangles2The Triangle Inequality
Can Three Sticks Meet?Exactly ReachingThe Range of the Third SideThe FormulaRecap: The Third Side5The Pythagorean Theorem
Squares on the SidesFinding the HypotenusePythagorean TriplesWhen It Is Not WholeRecap: The Hypotenuse8Special Right Triangles
The 45-45-90 TriangleLegs from the HypotenuseThe 30-60-90 TriangleAll Three SidesWhich Triangle Is It?Recap: Special Triangles11Two Tools at Once
Height of an IsoscelesArea from the HeightThe Equilateral TriangleRight Triangle PerimeterRecap: Two Tools3Perimeter
Around the EdgeA Missing SideIsosceles PerimeterSides as ExpressionsRecap: Around the Edge6Finding a Leg
Working BackwardsThe LadderWhich Side Is c?A Leg That Is Not WholeRecap: Finding a Leg