Find the shaded region

~54.54 units squared, or 25*pi - 24

Step-by-step explanation:

To find this, we need to find both the area of the triangle and circle, and then subtract the area of the triangle from the area of the circle.

Area of triangle:

Area of circle:

To find the radius, we first need to find the hypotenuse of the triangle, which happens to be the diameter of the circle.

Pythagorean Theorem: , where a and b are sides and c is the hypotenuse.

6^2 + 8^2 = c^2

36 + 64 = 100, c = 10

Knowing that the diameter is 10, we also know that the radius is 5.

Area of the circle with a radius of 5 is 25*pi, or 78.54~

Area of the triangle with side lengths of 6 and 8 is 24.

78.54 - 24 = 54.54 units squared.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source: