Question

Find the area of the region shaded in blue in the figure shown below. ​

Answer 1

Step-by-step explanation:

distance between (-2,-3) and (4,-1)

is the base of the triangle

and height will be anyway 6

so the base = √(36+4)

=√40

so area = 1/2*√40*6

=3√40

and the area of the rectangle = 12*6=72

so area of the shaded region is 72-3√40

Answer 2

Step-by-step explanation:

AREA OF SHADED REGION = AREA OF RECTANGLE - AREA OF THE TRIANGLE

SO,

Area of rectangle = LENGTH × BREDTH

= 12×6

= 72 unit²

AND,

Area of triangle is

here , we are given coordinates of triangle that is ,

(0,5) , (-2,-3) and (4,-1)

so , from formula we know that

Area of triangle =1/2 | x1 (y2-y3) + x2(y3-y1) + x3(y1-y2)|

HERE ,

X1 = 0 , X2 = -2 , X3 = 4

Y1 = 5 , Y2 = -3 , Y3 = -1

PUTTING THESE VALUES ON THE ABOVE FORMULA

WE HAVE ,

AREA OF TRIANGLE = 1/2 | 0 { -3 - (-1) } + (-2)(-1-5) + 4 {5- (-3) } |

AFTER CALCULATING WE HAVE ,

AREA OF TRIANGLE IS = 22 UNIT ²

NOW ,

AREA OF SHADED REGION IS = AREA OF RECTAGLE - AREA OF TRIANGLE

THAT IS ,

AREA OF SHADED REGION IS = 72 UNIT² - 22 UNIT²

SO,

AREA OF SHADED REGION IS = 50 UNIT²