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

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

jainveenamrata jainveenamrata · Answer 2 · 2022-08-17T14:48:21+02:00

The area of the shaded region in the polynomial form will be (x² + 11x + 30) / 2.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The width of the rectangle and triangle is (x + 6).

The height of the rectangle and triangle is (x + 5).

The area of the shaded region will be

Shaded Area = Area of rectangle - Area of triangle

Shaded Area = (x + 6)(x + 5) - (x + 6)(x + 5)/2

Shaded Area = (x + 6)(x + 5) / 2

Shaded Area = (x² + 6x + 5x + 30) / 2

Shaded Area = (x² + 11x + 30) / 2

The area of the shaded region in the polynomial form will be (x² + 11x + 30) / 2.

More about the geometry link is given below.

https://brainly.com/question/7558603

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