AREA OF A POLYGON

Area Of A Polygon

Definition Of Area Of A Polygon

Area of a Polygon is the amount of space or region occupied by that polygon.

More About Area of a Polygon

The area of an irregular polygon can be found by dividing it into different standard polygons.

Area of a square = s²

Area of a rectangle = lb

Area of a triangle = bh

Area of a parallelogram = bh

Area of a trapezoid = ()

Examples of Area of a Polygon

example of Area of a Polygon

Area of the figure = Area of rectangle ABCH + Area of rectangle DEFG = AH × AB + DE × EF = (6.5 × 4 + 3.5 × 9) m² = 57.5 m².
So, the area of the above irregular polygon is 57.5 m²

Video Examples: Area of Polygons

Solved Example on Area of a Polygon

Ques:

Find the area of the figure.

example of Area of a Polygon

Choices:

A. 14 ft²
B. 11 ft²
C. 12 ft²
D. 10 ft²
Correct Answer: D

Solution:

Step 1: The figure is divided into a trapezoid and a rectangle.
example of Area of a Polygon Step 2: Area of the figure = Area of trapezoid ABEF + Area of rectangle HCDJ
Step 3: = × FJ × (AF + BE) + HC × CD
Step 4: = × 1 × (3 + 5) + 2 × 3 = 10 [Substitute the values.]
Step 5: Therefore, area of the figure is 10 ft².

Quick Summary

Area of a polygon is the measure of the surface it covers.
Irregular polygons can be divided into standard polygons to calculate the total area.
Formulas exist for calculating the area of regular polygons like squares, rectangles, triangles, parallelograms, and trapezoids.

\[ Area depends on the specific polygon; examples include: \(A_{square} = s^2\), \(A_{rectangle} = lw\), \(A_{triangle} = \frac{1}{2}bh\) \]

🍎 Teacher Insights

Use visual aids and hands-on activities to demonstrate how to divide irregular polygons into regular shapes. Provide plenty of practice problems with varying levels of difficulty. Emphasize the importance of labeling units correctly.

🎓 Prerequisites

Basic arithmetic
Understanding of geometric shapes (squares, rectangles, triangles, parallelograms, trapezoids)
Concept of area

Check Your Knowledge

Q1: What is the area of a rectangle with length 5 cm and width 3 cm?

8 cm^2 15 cm^2 16 cm^2 20 cm^2

Q2: A square has a side length of 4 inches. What is its area?

8 in^2 12 in^2 16 in^2 20 in^2

Frequently Asked Questions

Q: How do you find the area of an irregular polygon?
A: Divide the irregular polygon into smaller, regular polygons (e.g., rectangles, triangles). Calculate the area of each regular polygon and then add the areas together.

Q: What is the difference between area and perimeter?
A: Area is the measure of the surface enclosed by a shape, while perimeter is the total length of the sides of the shape.

Q: Why is area measured in square units?
A: Area is measured in square units because it represents the number of squares of a certain size (e.g., 1x1 meter) that are needed to cover the surface.