Can someone please help me on this question! Thank you very much!!

(9√3 - 3π) cm²  or ≈ 6.16 cm²

Step-by-step explanation:

Refer to attached pictures

We have equilateral triangle with side of 6 cm and inscribed circle, we need to find the shaded area inside the triangle not covered by the circle.

The shaded are is the difference of areas of the triangle and circle

Area of equilateral triangle is calculated as per formula:

Area of circle is calculated as per formula:

Let's find the value of r:

Δ ADB is the right triangle with angles 30° and 60°

It has sides of 3 cm, 6 cm and AD= m cm

As per attached, m is the long leg and equal to a√3, so

also,

We can find AO in the same way as above using Δ AOF

AO= 2r as it is the hypotenuse and the hypotenuse is twice a short leg in the right triangle with angles 30° and 60°

So,  

Now we can get the area of circle:

Shaded are is:

attachment?

step-by-step explanation:

good luck on your studies! : )

david edward.