Question

Prove that area of triangle ​

Answer 1

Answer:

To derive the area of a rectangle, we use the unit squares. Divide the rectangle ABCD into unit squares, as shown. The area of a rectangle ABCD is the total number of unit squares contained within it. Thus, the total area of the rectangle ABCD is 48 sq.

Answer 2

Answer:

Let ABC be the the equilateral triangle with sides of equal length, a.

The median splits the equilateral triangle into two congruent right triangles (30°,60°,90°). The altitude and median are congruent in equilateral triangles.

The right triangles (30°,60°,90°) is a special triangle with ratio of sides:

1:√3:2 = shorter leg : longer leg : hypotenuse

½a:√3(½a):a = shorter leg : longer leg : hypotenuse

The longer leg is the altitude of the equilateral triangle.

h = √3(½a) = (√3/2)a = a•cos (30°) = a•sin (60°)

Area of equilateral triangle = ½×base×altitude = ½(a)(√3/2)a = (√3/4)a²

By Trigonometry

Area of equilateral triangle = ½(a)a•cos (30°) = ½a²•cos (30°) = (√3/4)a²

Area of equilateral triangle = ½(a)a•sin (60°) = ½a²•sin (60°) = (√3/4)a²

Step-by-step explanation:

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