CPM Homework Help : GC Problem 3-81

Enclosed polygon, resembling an upward arrow, comprised of a triangle, with rectangle centered on the bottom, with vertical dashed line down the middle of the arrow. Labels as follows: left slanted side is 10, left horizontal side is 4, right vertical side is 3, total bottom base side, 4. The dashed line at right represents the line of symmetry of the shaded figure. Find the area and perimeter of the shaded region. Show all work.

Hint:

Since you have been given the line of symmetry, you can now determine the lengths of all sides of the above figure.

Step 1:

Label all the sides that have been left blank. Orange Labels added to arrow, right slanted side, 10, right horizontal side 4, left vertical side, 3.

Step 2:

To find the perimeter, add up the values of all $7$ sides.

Step 3:

To find the area, split the shape into two separate parts. Outlines added: triangle in blue, rectangle in purple.

Step 4:

Find the area of each individual shape, then add the two together to find the area of the shape in its entirety.