Question

What is the area of the equilateral triangle with the length of each side equal to a? One-half a sine (60 degrees) 3 a sine (60 degrees) One-half a squared sine (60 degrees) a squared sine (60 degrees).

Answer 1

The area of an equilateral triangle can be written as a squared sine (60 degrees). Option D is correct.

What is an equilateral triangle?

The triangle in which all three sides are of the same length. In this the all angles are the same 60°.

The area of a triangle can be calculated by,

$A =\dfrac 12 \times b \times h$..................1

Where,

A - Area of triangle

b - base

h - height

From, Pythagoras Theorem

$a^2 = h^2 + (\dfrac a2)^2\\\\h^2 = a^2 - (\dfrac {a^2}4)\\\\h^2 = \dfrac {(3a2)}4$

Put the value of “h” in equation 1

$A =\dfrac 12 \times a \times \dfrac 12 \sqrt {3a}\\A =\dfrac { \sqrt 3}4 a^2$

Since √3/4 is equal to the sin60°.

So, $A =\rm \ sin60^o \ a^2$

Therefore, the area of an equilateral triangle can be written as a squared sine (60 degrees).

Learn more about the equilateral triangle?

https://brainly.com/question/14305983

Answer 2

Answer: C, 1/2a^2sin(60*)

Explanation:

if you scrolled to find a short answer same tbh