Respuesta :

valerieulbrich

Answer:

1.44 units²

Step-by-step explanation:

The angle for the big triangle is 60°, so the smaller triangle is 30°

so to find the base of the small triangle you can do tan 30 = X/2[tex]\sqrt{3}[/tex]

so x is 2, which means that the base of the big triangle is 4.

The area of the big triangle is 1/2bh = 1/2(4)(2[tex]\sqrt{3}[/tex]) = 4[tex]\sqrt{3}[/tex] = 6.93

Find hypotenuse (radius) using Pythagorean Theorem r = 4

The area of the piece of pie is [tex]\pi r^{2} *60/360[/tex] = 8.37

8.37 - 6.93 = 1.44

The shaded area is the difference between the area of the sector to the area of the triangle. Then the area of the shaded region is 1.08 square units.

What is a circle?

It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

Then the area of the shaded region will be

Shaded area = area of the sector - area of the triangle

The area of the sector will be

[tex]\rm Sector \ area = \dfrac{60}{360} \times \pi \times (2\sqrt3)^2\\\\Sector \ area = 6.28[/tex]

The area of the triangle will be

[tex]\rm Triangle \ area = \dfrac{1}{2} \times 1.732 \times 6\\\\Triangle \ area = 5.196[/tex]

Then the area of the shaded region will be

Shaded area = 6.28 - 5.196

Shaded area = 1.084 ≅ 1.08

More about the circle link is given below.

https://brainly.com/question/11833983

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