Question

Write a polynomial in standard form that represents the area of the shaded region.

Answer 1

Answer:

0.5x^2+5.5x+15

Step-by-step explanation:

So Imagine the two green triangles were put together to form one big triangle. This triangle is congruent, or the same as, the white triangle. This tells us that the rectangle minus the white triangle is the green triangle.

So we must first find the areas of the rectangle and the triangle.

Rectangle:

A=bh

b=x+6

h=x=5

A=(x+6)(x+5)

Use FOIL method (First, Outside, Inside, Last (multiply thee terms together)

First: x(x)=x^2

Outside: x(5)=5x

Inside: 6(x)=6x

Last: 5(6)=30

So, x^2+5x+6x+30

or in simplest terms x^2+11x+30

Triangle:

A=1/2bh

So take (x^2+11x+30)/2

1/2x^2+5.5x+15

Since we already determined the triangles were congruent, or the same, we can conclude that this is our answer

x^2=x to the power of two or x squared