What is the area of this figure?
Understand the Problem
The question asks for the area of a compound figure, which can be found by dividing the figure into rectangles and calculating the area of each, then sum them up. The compound figure consists of two rectangles. We must calculate the area of each and then add them.
Answer
$29 \text{ mm}^2$
Answer for screen readers
$29 \text{ mm}^2$
Steps to Solve
- Identify the two rectangles
The figure can be divided into two rectangles: one with dimensions 7 mm x 3 mm, and another with dimensions 2 mm x 4 mm.
- Calculate the area of the first rectangle
The area of a rectangle is length times width.
$$ Area_1 = 7 \text{ mm} \times 3 \text{ mm} = 21 \text{ mm}^2 $$
- Calculate the area of the second rectangle
Again, the area of a rectangle is length times width.
$$ Area_2 = 2 \text{ mm} \times 4 \text{ mm} = 8 \text{ mm}^2 $$
- Calculate the total area
Add the areas of the two rectangles to find the total area of the compound figure.
$$ Area_{total} = Area_1 + Area_2 = 21 \text{ mm}^2 + 8 \text{ mm}^2 = 29 \text{ mm}^2 $$
$29 \text{ mm}^2$
More Information
The total area of the compound figure is found by dividing it into simpler shapes (rectangles in this case), calculating the area of each shape, and then summing those areas together.
Tips
A common mistake is to misidentify the dimensions of the rectangles or to incorrectly apply the area formula. Another common mistake is to add all provided numbers together. Carefully examine the diagram to determine the correct dimensions and make sure to only include the areas of our rectangles and not any other values.
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