Questions: What is the area of this figure? Write your answer using decimals, if necessary. square millimeters

Solution Steps

The figure is composed of three rectangles and one right triangle.

The first rectangle has dimensions 3 mm by 4 mm. \[ \text{Area} = 3 \, \text{mm} \times 4 \, \text{mm} = 12 \, \text{mm}^2 \]

The second rectangle has dimensions 2 mm by 4 mm. \[ \text{Area} = 2 \, \text{mm} \times 4 \, \text{mm} = 8 \, \text{mm}^2 \]

The third rectangle has dimensions 3 mm by 2 mm. \[ \text{Area} = 3 \, \text{mm} \times 2 \, \text{mm} = 6 \, \text{mm}^2 \]

The right triangle has a base of 9 mm and a height of 6 mm. \[ \text{Area} = \frac{1}{2} \times 9 \, \text{mm} \times 6 \, \text{mm} = 27 \, \text{mm}^2 \]

Add the areas of all the shapes to find the total area. \[ \text{Total Area} = 12 \, \text{mm}^2 + 8 \, \text{mm}^2 + 6 \, \text{mm}^2 + 27 \, \text{mm}^2 = 53 \, \text{mm}^2 \]

Final Answer