Equilateral triangle and square
Q01. Diagram
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Q02. Equilateral triangle and square
Construction
- Draw an equilateral triangle
- Draw a square
- Let each side be 1
- Height of triangle = Sqr(3)/2
- Find ration of area of square to triangle
Solution
- Angle A = 60 degrees
- Right angle triangle APS, angle APS = 30 degrees
- Hence AS = (AC/2)/2 = 1/4
- Hence S is mid point of AC
- Since PS parallel to height, hence P is mid point of AC
- Hence PS = height/2 = h/2
- Area of triangle
- = (AB*h)/2
- = (1*Sqr(3)/2)/2
- = Sqr(3)/4
- Area of square
- = PS^2 = (h/2)^2
- = (Sqr(3)/4)^2
- = 3/16
- Ratio of square area to triangle area
- = (3/16)/(Sqr(3)/4)
- = Sqr(3)/4
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Q03. Questions
Questions
- 1. Right angle triangle, side opposite 30 degree angle is half of hypothese
- 2.
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