Find the area of each of the following polygons by doing...

Find the area of each of the following polygons by doing each of the following steps:
a) Copy the figure.
b) Draw an altitude.
c) Find the length of the altitude.
d) Find the area of the polygon.
(FIGURE CAN'T COPY)

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Key Concepts

Polygon

A polygon is a closed, two-dimensional figure made up of a finite chain of straight line segments that are connected end-to-end. Understanding its properties, such as side lengths and angles, is essential for determining measures like area, especially when the shape is irregular or compound.

Altitude

An altitude in a polygon is a perpendicular segment drawn from a vertex to the line containing the opposite side (or base). It represents the height necessary for calculating the area of figures such as triangles or other polygons when using base-height formulas.

Area Calculation

Calculating the area of a polygon often involves identifying a base and its corresponding altitude (height), then applying the appropriate formula. For instance, the area of a triangle is computed as one-half the product of its base and height, with similar approaches adapted for other polygon types.

Decomposition

Decomposition is the technique of breaking a complex polygon into simpler shapes, such as triangles or rectangles, whose areas are easier to calculate. This method is particularly useful when a direct application of a single area formula is not possible due to the figure’s complexity.

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