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A planar shape or solid that is inscribedin another geometric shape or solid is enclosed and "fitted tightly" within it. Saying "a square is inscribed in a triangle" means exactly the same thing as "a triangle is circumscribed in a square".
The largest square that can be inscribed in an equilateral triangle− The largest square that can be inscribed in an equilateral triangle−Let Let’s take an example,Input: 5 Output: 2.32explains that one side of the square is
x.
Now,AH is perpendicular to DE.
DE is parallel to BC, angle AED = angle ACB = 60
is in triangleEFC中,
⇒ Sin60 = x/ EC ⇒ √3 / 2 = x/EC ⇒ EC = 2x/√3at In triangleAHE,
⇒ Cos 60 = x/2AE ⇒ 1/2 = x/2AE ⇒ AE = x Sides of a triangleAC = 2x/√3 x. Now,
a = 2x/√3 x
x = a/(1 2/√3) = 0.464a
Example Demonstration#include <stdio.h> #include <math.h> int main() { float a = 5; float area = 0.464 * a; printf("The area is : %f",area); return 0; }Output
The area is : 2.320000
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