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gulaghasi [49]
3 years ago
15

Trapezoid A B C D is shifted down and to the left to form trapezoid A prime B prime C prime D prime. Trapezoid A prime B prime C

prime D prime is rotated 270 degrees about point B. What is the final transformation in the composition of transformations that maps pre-image ABCD to image A"B'C"D"? a translation down and to the right a translation up and to the right a 270° rotation about point B' a 180° rotation about point B'
Mathematics
2 answers:
iVinArrow [24]3 years ago
7 0

Answer:

d

Step-by-step explanation:

9966 [12]3 years ago
6 0

Answer:

d

Step-by-step explanation:

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Brums [2.3K]

The area of the shaded region is  \rm (150\sqrt{3} \ - 75\pi ) \ feet^2 option first is correct.

It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.

It is required to find the shaded area (missing data is attached shown in the picture).

<h3>What is a circle?</h3>

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a hexagon with a side length of 10 feet.

We know the area of the hexagon is given by:

\rm A = \frac{3\sqrt{3} }{2} a^2  where a is the side length.

\rm A = \frac{3\sqrt{3} }{2} 10^2 ⇒ 150\sqrt{3} \rm feet^2

We have the shortest length = x feet and from the figure:

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The radius of the circle r = longer leg

\rm r = x\sqrt{3} \Rightarrow 5\sqrt{3} feet

The area of the circle a = \pi r^2  ⇒ \pi (5\sqrt{3} )^2 \Rightarrow 75\pi \ \rm feet^2  

The area of the shaded region = A - a

\rm =(150\sqrt{3} \ - 75\pi ) \ feet^2

Thus, the area of the shaded region is  \rm (150\sqrt{3} \ - 75\pi ) \ feet^2

Learn more about circle here:

brainly.com/question/11833983

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