Area is a measure of the size or extent of a two-dimensional surface or region. It quantifies the amount of space occupied by a flat shape or the surface of an object.
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The area of a rectangle is calculated by multiplying its length and width.
The area of a triangle is calculated by multiplying its base and height, and then dividing the result by 2.
The area of a trapezoid is calculated by adding the lengths of the parallel bases and multiplying the result by the height, and then dividing by 2.
The area of a circle is calculated by multiplying the square of its radius by $\pi$.
The area of an irregular figure can be approximated by dividing it into smaller, simpler shapes and calculating the area of each, then adding them together.
Review Questions
How is the area of a rectangle calculated, and how does this relate to the properties of rectangles discussed in Topic 9.4?
The area of a rectangle is calculated by multiplying its length and width. This relates to the properties of rectangles discussed in Topic 9.4 because the length and width are key dimensions that define the shape of a rectangle. Understanding how to calculate the area of a rectangle is essential for solving geometry applications involving rectangles, as the area calculation is often required to determine the size or dimensions of a rectangular shape.
Explain how the area of a triangle is calculated, and describe how this relates to the properties of triangles discussed in Topic 9.4.
The area of a triangle is calculated by multiplying its base and height, and then dividing the result by 2. This relates to the properties of triangles discussed in Topic 9.4 because the base and height are fundamental dimensions that define the shape of a triangle. Knowing how to calculate the area of a triangle is essential for solving geometry applications involving triangular shapes, as the area calculation is often required to determine the size or dimensions of a triangular figure.
Discuss how the area of a circle is calculated, and explain how this relates to solving geometry applications involving circles, as discussed in Topic 9.5.
The area of a circle is calculated by multiplying the square of its radius by $\pi$. This relates to solving geometry applications involving circles, as discussed in Topic 9.5, because the area of a circle is a fundamental property that is often required to determine the size or dimensions of a circular shape. Understanding how to calculate the area of a circle and applying this knowledge to solve real-world geometry problems is a key skill covered in this topic.
The three-dimensional measure of the amount of space occupied by an object, typically measured in cubic units such as cubic inches or cubic centimeters.
Dimension: A measure of the size of an object in a particular direction, such as length, width, or height.