What is the area of the shaded region in the figure below? Round your answer to the nearest square centimeter.

ng8165 Apr 7, 2019

#1**+1 **

Oh I just found the answer:

The two triangles that are shaded blue are similar.

So we have the following ratios:

3/3+9 = x/9

x=9/4

So height of the black triangle is 9 - 9/4 = 27/4

So area of black triangle is (9 * 27/4)/2 = 243/8

EDIT: here's the image

ng8165 Apr 7, 2019

#2**+1 **

Let the bottom left vertex of the small square be located at (0,0)

Let the top right vertex of the large square be located at (12, 9)

So....the equation of the line connecting these two points is y = (9/12) x ⇒ y = (3/4)x (1)

The right edge of the small square lies on the line x = 3 (2)

So....subbing (2) into (1) we have that

y = (3/4)(3) = 9/4

Then....the height of the shaded area = 9 - 9/4 = 27/4 cm

And the width of the shaded area = 9 cm

And since the shaded area is triangular, its area =

(1/2) width * height =

(1/2)(9)(27/4) =

(9/2)(27/4) =

243/8 cm^2 =

30.375 cm^2

CPhill Apr 7, 2019