Question

Finding the area of a polygon

Answer 1

To find the area of a polygon, follow these steps:

1. Identify the type of polygon you are dealing with. Different polygons have different formulas for finding their areas. Some common polygons include triangles, rectangles, squares, parallelograms, and trapezoids.

2. For regular polygons (polygons with equal sides and angles), you can use a specific formula to find their areas. For example, to find the area of a regular triangle, you can use the formula: Area = (base × height) ÷ 2.

3. For irregular polygons, where the sides and angles are not equal, you can divide the polygon into smaller shapes, such as triangles or rectangles, whose areas you can calculate easily. Then, add up the areas of these smaller shapes to find the total area of the polygon.

4. Use the appropriate formula for each smaller shape. For example, to find the area of a rectangle, you can use the formula: Area = length × width. To find the area of a triangle, you can use the formula: Area = (base × height) ÷ 2.

5. Once you have calculated the areas of the smaller shapes, add them up to find the total area of the polygon.

6. Remember to include the units of measurement in your answer. For example, if the sides of the polygon are measured in centimeters, the area will be in square centimeters.

Let's take an example:

Suppose you have an irregular polygon with sides measuring 5 cm, 8 cm, and 10 cm. You can divide this polygon into two triangles. First, find the area of each triangle using the formula: Area = (base × height) ÷ 2.

Triangle 1: Base = 5 cm, Height = 8 cm. Area = (5 cm × 8 cm) ÷ 2 = 20 cm².

Triangle 2: Base = 10 cm, Height = 8 cm. Area = (10 cm × 8 cm) ÷ 2 = 40 cm².

Add up the areas of the two triangles: 20 cm² + 40 cm² = 60 cm².

So, the total area of the irregular polygon is 60 square centimeters.

Remember to adapt the steps and formulas to the specific type of polygon you are dealing with.

Answer 2

To figure out the area of a Polygon you can use various methods depending on the type of polygon.

⇾ For regular polygons, you can use specific formulas

⇾ For irregular polygons, you can divide them into simpler shapes and sum up their areas.

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Polygon

➥ A polygon is a closed two-dimensional shape with straight sides.

# It is formed by connecting multiple line segments together to create a closed figure.

# Polygons can have any number of sides, but they must have at least three sides.

# Common examples of polygons include triangles, squares, rectangles, pentagons, hexagons, and so on.

Types of Polygon

• Regular Polygon :-

➥ A regular polygon is a polygon where all sides are of equal length and all interior angles have the same measure.

Eg : equilateral triangles, squares, and regular hexagons.

• Irregular Polygon :-

➥ An irregular polygon is one that has sides and angles of different lengths and measures. Its sides and angles are not all equal.

• Convex Polygon :-

➥ A convex polygon is a polygon in which all interior angles are less than 180 degrees.

• Concave Polygon :-

➥ A concave polygon is a polygon with at least one interior angle greater than 180 degrees.

# It has a portion that is "caved in," which means that a line segment connecting two points inside the polygon can cross the boundary.