Answer:
51.5 units squared
Step-by-step explanation:
We want to find the area of this strange composite figure. One way to do this is to extend AB past A to hit the y-axis; doing so, we have a big rectangle with dimensions of 8 by 11 units. We can then subtract the non-red parts from the area of the big rectangle.
Draw a vertical line from E to the x-axis, splitting the non-shaded region made up of points F, E, D, C and the origin into two trapezoids.
The area of a trapezoid is denoted as A = (1/2) * (b1 + b2) * h, where b1 and b2 are the parallel bases and h is the height.
In the first trapezoid with points F and E, the two bases are 3 and 6, and the height is 4. So the area is:
A = (1/2) * (b1 + b2) * h
A = (1/2) * (3 + 6) * 4 = 18 units squared
The second trapezoid with points E, D, and C has bases 2 and 7 and height 3. So the area is:
A = (1/2) * (b1 + b2) * h
A = (1/2) * (2 + 7) * 3 = 27/2 = 13.5 units squared
The last piece of unshaded region is the right triangle at the bottom left hand corner. It has a base of 5 and height 2, so the area, which is denoted as A = (1/2) * b * h, is:
A = (1/2) * b * h
A = (1/2) * 5 * 2 = 5 units squared
Add up the areas of all the unshaded regions:
18 + 13.5 + 5 = 36.5 units squared
The giant rectangle's area is denoted by A = lw, where l is the length and w is the width. The length is 8 and the width is 11. So the area is:
A = lw
A = 8 * 11 = 88 units squared
Subtract the unshaded area from 88:
88 - 36.5 = 51.5
The area is thus 51.5 units squared.
<em>~ an aesthetics lover</em>
