Extended Distributive Property: Distributive property in geometry

Look at the rectangle in the figure below. What is its area?

What do a and x need to be for the rectangle to exist?

Area:

$12x^2-15x-4ax+5a$

Conditions:

x > 1\frac{1}{4}

3x>a

Look at the circle in the figure.

$r=7-5a$

What is the area of the circle?

$25\pi a^2-70\pi a+49\pi$

What is the area of the trapezoid in the figure?

$h=(12x-8)$

$84x^2-38x-12$

Look at the triangle in the figure.

$h=x-5$

What is the area of the triangle in terms of x?

$1\frac{1}{2}x^2-3.5x-20$

Look at the rectangles in the diagram below.

Which has a larger area and by how much?

The area of rectangle A is larger by 2 area units.