Question

What is the area of the equilateral triangle with the length of each side equal to a?

Answer 1

its the 3rd one !! 1/2a^2 sin 60

Answer 2

(C)

Explanation:

From the given figure, it can be seen that the all the sides of the triangle are equal and are equal to a.

Now, area of the equilateral triangle is given as:

`A=(√(3))/(4)a^2`

Now, we know that
`sin60^(\circ)=(√(3))/(2)`

then, (A)
`(1)/(2)asin60^(\circ)=(√(3))/(4)a`

which is not equal to the value of area of equilateral triangle, thus this option is not correct.

(B)
`3asin60^(\circ)=(3√(3))/(2)a`

which is not equal to the value of area of equilateral triangle, thus this option is not correct.

(C)
`(1)/(2)a^2sin60^(\circ)=(√(3))/(4)a^2`

which is equal to the value of area of equilateral triangle, thus this option is correct.

(D)
`a^2sin60^(\circ)=(√(3))/(2)a^2`

which is not equal to the value of area of equilateral triangle, thus this option is not correct.