Answer:
15.59 inches²
Step-by-step explanation:
Area of a triangle = [tex]\frac{1}{2}[/tex] (base) × (height)
Base of the triangle = 6 inches = BC
so BD = CD = 3 inches
Now height h = AD = [tex]\sqrt{6^{2}- 3^{2} }[/tex] [ By Pythagoras theorem ]
h = [tex]\sqrt{36-9}[/tex]
= [tex]\sqrt{27}[/tex]
= [tex]\sqrt[3]{3}[/tex]
Now area of equilateral triangle ABC
= [tex]\frac{1}{2}[/tex] (6) ( [tex]\sqrt[3]{3}[/tex])
= 3 × ([tex]\sqrt[3]{3}[/tex])
= [tex]\sqrt[9]{3}[/tex] inches²
≈ 15.59 inches²
