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An **inscribed** planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid. To say that "square is inscribed in triangle" means precisely the same thing as *"triangle is circumscribed about square"*.

Biggest Square that can be inscribed within an Equilateral triangle −

Biggest Square that can be inscribed within an Equilateral triangle −

Let’s take an example,

Input: 5 Output: 2.32

The side of the square be **x**.

Now, **AH** is perpendicular to **DE**.

**DE** is parallel to **BC**, angle **AED = angle ACB = 60**

In triangle **EFC**,

⇒ Sin60 = x/ EC

⇒ √3 / 2 = x/EC

⇒ EC = 2x/√3

In triangle **AHE**,

⇒ Cos 60 = x/2AE

⇒ 1/2 = x/2AE

⇒ AE = x

side **AC** of the triangle = **2x/√3 + x**. Now,

**a = 2x/√3 + x**

**x = a/(1 + 2/√3) = 0.464a**

#include <stdio.h> #include <math.h> int main() { float a = 5; float area = 0.464 * a; printf("The area is : %f",area); return 0; }

The area is : 2.320000

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