CPM Homework Help : ACC6 Problem 8-54

Find the area of the shape below. All angles are right angles.

An enclosed figure: Starting at the upper left corner: right 6 cm, down 15 cm, right, an unknown amount, up, an unknown amount, right 9 cm, down 9 cm, left 24 cm, up 18 cm to enclose the figure.

Step 1:

To find the area of the entire shape, separate it into rectangles.

Step 2:

One way to divide the shape up is to make a $6$ cm by $15$ cm rectangle, a $9$ cm by $9$ cm square, and a rectangle with unknown sides. To find its length, you must subtract the $9$ cm side from the $24$ cm parallel to it. To find its width, you must subtract the vertical $15$ cm side from $18$ cm side.

The same figure with a horizontal rectangle drawn in the lower left corner, with the top edge as the unknown horizontal side, extended to the left, the right edge as the unknown vertical side, extended down, bottom edge label 15 cm.

$24\text{ cm}-9\text{ cm}=15\text{ cm}$
$18\text{ cm}-15\text{ cm}=3\text{ cm}$

Step 3:

Find the areas of the rectangles and add them together.

$(6 \text{ cm} × 15 \text { cm}) + (9 \text{ cm} × 9 \text{ cm}) + (15 \text{ cm} × 3 \text{ cm}) = ?$

Answer:

The area of the shape is $216$ square centimeters.