Questions: By considering total area as the sum of the areas of all of its parts, we can determine the area of a figure such as the one shown to the right. Find the total area of the figure to the right. A= (Simplify your answer.) units ^2

Solution Steps

The figure consists of a parallelogram and a triangle. The parallelogram has a base of 9 units and a height of 6 units. The triangle has a base of 9 units and a height of 3 units.

The area of a parallelogram is given by the formula: \[ \text{Area}_{\text{parallelogram}} = \text{base} \times \text{height} \] \[ \text{Area}_{\text{parallelogram}} = 9 \times 6 = 54 \, \text{units}^2 \]

The area of a triangle is given by the formula: \[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} \] \[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times 9 \times 3 = \frac{1}{2} \times 27 = 13.5 \, \text{units}^2 \]

Add the areas of the parallelogram and the triangle to find the total area of the figure: \[ \text{Total Area} = \text{Area}_{\text{parallelogram}} + \text{Area}_{\text{triangle}} \] \[ \text{Total Area} = 54 + 13.5 = 67.5 \, \text{units}^2 \]

Final Answer