what is the area of this figure?\nwrite your answer using decimals, if necessary.\nsquare centimeters

Explanation:

Step1: Split figure into 3 parts

Divide the shape into a rectangle, a square, and a right triangle.

Step2: Calculate area of rectangle

The rectangle has dimensions $4\ \text{cm} \times 6\ \text{cm}$. $\text{Area}_1 = 4 \times 6 = 24\ \text{cm}^2$

Step3: Calculate area of square

The square has side length $2\ \text{cm}$. $\text{Area}_2 = 2 \times 2 = 4\ \text{cm}^2$

Step4: Calculate area of triangle

The triangle has base $6\ \text{cm}$ and height $9-6=3\ \text{cm}$. $\text{Area}_3 = \frac{1}{2} \times 6 \times 3 = 9\ \text{cm}^2$

Step5: Sum all areas

Add the areas of the three parts. $\text{Total Area} = 24 + 4 + 9$

Answer:

37 square centimeters