Which sentence describes a way to determine the area of the polygon shown? Find the area of a rectangle and then subtract the area of a triangle. Find the area of the shaded polygo... Which sentence describes a way to determine the area of the polygon shown? Find the area of a rectangle and then subtract the area of a triangle. Find the area of the shaded polygon. Area of polygon = square units.
Understand the Problem
The question asks how to find the area of a shaded polygon by using the area of a rectangle and subtracting the area of a triangle. It also requests the actual area of the shaded polygon to be calculated based on this method.
Answer
The area of the polygon is $20$ square units.
Answer for screen readers
The area of the shaded polygon is $20$ square units.
Steps to Solve
- Finding the Area of the Rectangle
First, identify the dimensions of the rectangle. From the grid, the rectangle appears to be 6 units wide and 4 units tall. The area of the rectangle can be calculated using the formula:
$$ \text{Area}_{\text{rectangle}} = \text{width} \times \text{height} $$
So,
$$ \text{Area}_{\text{rectangle}} = 6 \times 4 = 24 \text{ square units} $$
- Finding the Area of the Triangle
Next, determine the dimensions of the triangle that will be subtracted from the rectangle. The triangle has a base of 4 units and a height of 2 units. The area can be calculated using the formula:
$$ \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} $$
Thus,
$$ \text{Area}_{\text{triangle}} = \frac{1}{2} \times 4 \times 2 = 4 \text{ square units} $$
- Calculating the Area of the Shaded Polygon
Finally, calculate the area of the shaded polygon by subtracting the area of the triangle from the area of the rectangle:
$$ \text{Area}{\text{polygon}} = \text{Area}{\text{rectangle}} - \text{Area}_{\text{triangle}} $$
Therefore,
$$ \text{Area}_{\text{polygon}} = 24 - 4 = 20 \text{ square units} $$
The area of the shaded polygon is $20$ square units.
More Information
To find the area of a complex polygon, one common method is to calculate the area of a larger shape (like a rectangle) and then subtract the areas of any smaller shapes (like triangles) that are excluded from the shaded region.
Tips
- Forgetting to convert the dimensions correctly. Make sure to double-check that the dimensions used for calculations are accurate.
- Using incorrect formulas for area calculations. It's essential to know the correct formula for both rectangles and triangles.
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