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2-46.

Find the area and perimeter of the figure at right. All angles are right angles. Show all of your work.

An enclosed figure (units in centimeters): Starting at the upper left corner: right an unknown number, down an unknown number, right 3, up 2, right 4, down 5, left 10, and up 10, to enclose the figure.

First, remember that the perimeter of a figure is the sum of the lengths of all the sides.

To find the perimeter, it would be helpful to find the unknown lengths of the sides (represented as and at right).

Labels added to the unknown sides, top edge, a, right top side, b.

The top edge is  the bottom length 10 cm minus the other horizontal lengths (3 cm and 4 cm).

To find the unknown vertical side, look at all of the vertical lengths, cm, cm, and cm. How do these lengths help you find the unknown side?

One way to find the area is to divide the figure into small squares of the same size. Here, you should use squares with sides of one centimeter like in the figure on the right. Now you can count the squares to find the area.

Interior rectangles divided into squares, as follows: left vertical rectangle, 10 rows of 3 squares, bottom horizontal rectangle, (overlaps with left rectangle, 3 rows of 10 squares, right vertical rectangle, (overlaps with bottom rectangle), 5 rows of 4 squares.

Using the formula Area = (length)(width), you can also easily find the area. First, divide the figure into separate rectangles and then find the individual areas with the formula mentioned before.

Interior divided into 3 vertical rectangles, so that every vertical side continues through the to the bottom edge, & is a divider.

Don't forget to add all of the areas together!

Labels added to the 3 vertical rectangles, left, 30 square cm, middle, 9 square cm, right, 20 square cm.