Question

the diagonal of a square is equal to the side of an equilateral triangle.if the area of the square is 18√359 cm. what is the area in cm²of the equilateral triangle.
​

Answer 1

Required Answer :

Area of equilateral triangle = 294.29 cm²

Given :

• Diagonal of a square is equal to the side of an equilateral triangle
• Area of square = 18√359 cm²

To find :

• Area of equilateral triangle

Solution :

Using formula,

• Area of square = side²

Substituting the given values :-

→ 18√359 = side ²

→ Taking square root on both the sides :-

→ √(18√359) = side

→ √18(18.9) = side

→ √340.2 = side

→ 18.44 = side

Side of the square = 18.44 cm

Using formula,

• Diagonal of square = √2a

Substituting the given values :-

→ Diagonal of square = √2 × 18.44

→ Diagonal of square = 26.07

Diagonal of square = 26.07 cm

Diagonal of square = Side of equilateral triangle

Hence, side of equilateral triangle = 26.07 cm

Using formula,

• Area of equilateral triangle = √3/4 a²

Substituting the given values :-

→ Area of equilateral triangle = √3/4 × (26.07)²

→ Area of equilateral triangle = √3/4 × 679.64

→ Area of equilateral triangle = 294.29

Therefore, the area of equilateral triangle = 294.29 cm²