What is the area of a rectangle with vertices at (−6, 3)(−6, 3) , (−3, 6)(−3, 6) , (1, 2)(1, 2) , and (−2, −1)(−2, −1) ? do not round any side lengths.

Well, find the legnth and width because lenth times width =area
we just need to find 2 differnd distances

the distance between 2 points, (x1,y1) and (x2,y2) is

let's find distance between (-6,3) and (-3,6)
=√18=3√2

the other one
from (-3,6) to (1,2)
=√32=4√2

area=legnth times width
legnth=4√2
width=3√2
area=4√3 times 3√2=12*2=24

the area is 24

solution: - consider a rectangle   with dimensions 12cm×2cm

then its area =   length×breadth = 12cm × 2cm =24 sqcm

now consider a circle with radius r= 8 cm

we know that area of a circle =

as the rectangle   is lying inside the circle as in figure

the area of the remaining part(or the shaded region)   =area of circle -area of rectangle

answer- the area of the shaded region is