The figure below is made up of a rectangle WUVY and a square WXYZ. The length of WZ is 8 cm. What is the area of the whole figure? Answer: ___ $\text{cm}^2$

1. Calculate the area of the square $WXYZ$ and the triangle $WXY$.

Area of square $WXYZ = 8 \times 8 = 64 \text{ cm}^2$
Area of triangle $WXY = \frac{1}{2} \times 64 = 32 \text{ cm}^2$

2. Relate the area of triangle $WXY$ to the area of rectangle $WUVY$.

Triangle $WXY$ and rectangle $WUVY$ share the same base $WY$.
Since $X$ lies on the line $UV$ which is parallel to $WY$, the perpendicular height of triangle $WXY$ from $X$ to $WY$ is equal to the width of the rectangle $WUVY$.
Therefore, Area of rectangle $WUVY = 2 \times \text{Area of triangle } WXY = 2 \times 32 = 64 \text{ cm}^2$.

3. Calculate the area of the whole figure.

The whole figure is made up of triangle $WZY$ and rectangle $WUVY$.
Area of triangle $WZY = 32 \text{ cm}^2$
Total area = $32 + 64 = 96 \text{ cm}^2$