Question

Find the area of an equilateral triangle with a side of 6 inches

Answer 1

Explanation:

the answer would be 7.5

Answer 2

15.59 inches²

Explanation:

Area of a triangle =
`(1)/(2)` (base) × (height)

Base of the triangle = 6 inches = BC

so BD = CD = 3 inches

Now height h = AD =
`\sqrt{6^(2)- 3^(2) }` [ By Pythagoras theorem ]

h =
`√(36-9)`

=
`√(27)`

=
`\sqrt[3]{3}`

Now area of equilateral triangle ABC

=
`(1)/(2)` (6) (
`\sqrt[3]{3}`)

= 3 × (
`\sqrt[3]{3}`)

=
`\sqrt[9]{3}` inches²

≈ 15.59 inches²