*ANSWER ASAP , 0SEE ATTACHMENTS BELOW* What is the area of the polygon?

Solution,

A( 1,4)

B(3,6)

C(8,4)

D(3,2)

Now,

Finding the distance of A and C

A(1,4)----->(X1, y1)

C (8,4)---->(x2, y2)

AC :

√(x2,X1)^2+ (y2-y1)^2

AC = 7 units

By connecting BD, we get 2 triangles

i.e ∆ABD and ∆ BCD

Total area of polygon

= Area of ∆ ABD + Area of ∆ BCD

Area of ∆ABD

= 1/2 * base *height

= 1/2* BD * AO

= 1/2*4*2

= 4 units

Again,

Area of ∆BCD

= 1/2* base* height

= 1/2 * BD*CO

= 1/2*4*5

= 10 units

Total area:

= Area of ∆ ABD + Area of ∆ BCD

= 4 units +10 units

= 14 units

Hope this helps...

Good luck on your assignment..