Find the area of the following shape. You must show all work to receive credit. (10 points) Figure ABCDEF is shown.

53

Step-by-step explanation:

1) Take the area of the rectangle from origin to Point B. We see that it is 8 * 11 = 88 units of area

2) We subtract all the triangles in the rectangle that are not covered by the shape.

So

Take the area of the big imaginary rectangle and subtract the area of all the smaller triangles and the smaller rectangle

88 - 5 - 6 - 7.5 - 18 = 51.5

Done!

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.

~ an aesthetics lover

-232

step-by-step explanation: