Question

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

Answer 1

To find the polynomial that represents the area of the shaded region, determine the dimensions of the shaded region and write the polynomial in standard form.

Step-by-step explanation:

To find the polynomial that represents the area of the shaded region, we need to determine the dimensions of the shaded region. Once we have the dimensions, we can write the polynomial in standard form.

Let's say the length of the shaded region is 'L' units and the width is 'W' units. The area of the rectangle is given by the equation: A = L * W. The area of the triangle is given by the equation: A = 0.5 * base * height.

Add these two equations together to get the polynomial that represents the area of the shaded region: A = L*W + 0.5*base*height.

Answer 2

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