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3 years ago

What is the area of the shaded region of the circle?

Mathematics

1 answer:

eduard3 years ago

6 0

Answer:

12π ft², B

Step-by-step explanation:

Area of circle: radius²π

The area of the entire circle would thus be 6²π, or 36π

Note that a circle has a total degree measure of 360°, and the shaded area is 120°. Thus, the area of the shaded region would be 120/360 of the circle's area, or 1/3.

1/3 * total area of the circle = area of the shaded region

1/3 * 36π = 12π

Thus, the answer is 12π ft², or B.

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On a coordinate plane, triangles R S T and L M N are shown. Triangle R S T has points (5, 5), (2, 1), and (1, 3). Triangle L M N

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Answer:

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Step-by-step explanation:

Given

RST

$R =(5,5)$

$S= (2,1)$

$T = (1,3)$

LMN

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$N= (-2,-3)$

Required

Compare both areas

The area of triangle is:

$Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|$

For RST, we have:

$Area = \frac{1}{2}|5*1 - 2*5 + 2*3 - 1*1 + 1*5 - 5*3|$

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Remove absolute signs

$Area = \frac{1}{2}*10$

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For LMN, we have:

$Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|$

$Area = \frac{1}{2}|0*-4-2*-1+2*-3--2*-4--2*-1-0*-3|$

$Area = \frac{1}{2}|-14|$

Remove absolute signs

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<em>By comparing both areas, we can conclude that LMN has a larger area</em>

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