Question

Find the area of the shaded portion of the triangle if length of each side is 2cm, and area of the eye is 1cm²​

Answer 1

Answer:

$\boxed{\underline{\huge{\mathtt{\sqrt{3} - 1 cm}}}}$

Explanation:

$\text{Area of the shaded region of the triangle = Area of the Triangle - Area of the eye}\\\text{Here,}\\\text{We already have the area of the eye = 1 cm}^\text{2}\\\\\text{We have been given that the three sides of the triangle are equal, i.e., 2 cm}\\\therefore\text{Area of the Triangle, A}_1 = \dfrac{\sqrt{3}}{4}a^2 \text{ [Heron's Formula]}\\= \dfrac{\sqrt{3}}{4}\times2^2 = \dfrac{\sqrt{3}}{\cancel{4}} \times \cancel{4} = \sqrt{3} \text{ cm}^2\\\\\text{Area of the eye, A}_2 = \text{1 cm}^2$$\text{Area of the shaded region}=A_1-A_2=\underline{(\sqrt{3}-1)\text{ cm}^2}$