Area of a Polygon
In this section, we learn how to calculate the area of polygons by breaking them down into simpler shapes. For instance, we can divide a quadrilateral into triangles, allowing us to apply previously learned area formulas. The area of a polygon can often be determined through identifying its parts, calculating their individual areas, and then summing these values.
Key Concepts:
- Decomposition: The primary strategy involves cutting complex shapes into familiar ones like triangles and trapeziums. This method makes calculations feasible and often easier to visualize.
- Areas of Basic Shapes: Understanding how to calculate the area of triangles and trapeziums is crucial. We utilize formulas such as:
- Area of a triangle = 1/2 * base * height
- Area of a trapezium = 1/2 * (sum of parallel sides) * height
- Practical Applications: The section includes tasks to find the area of irregular polygons by applying the decomposition strategy, illustrated through several examples, such as finding the area of a trapezium-shaped field or a pentagonal park.
- Exercises: The section is rich in exercises that challenge students to apply their knowledge, ensuring comprehension of the area concept and calculation methods.
Thus, the area of polygons can be effectively determined using decomposition techniques and well-understood formulas, fostering a strong geometric intuition.
Example 2:
The area of a trapezium-shaped garden is 600 m², the distance between two parallel sides is 10 m and one of the parallel sides measures 25 m. Find the other parallel side.
Solution: Let one of the parallel sides of the trapezium be \( a = 25 \) m, and the other parallel side be \( b \), height \( h = 10 \) m.
The given area of the trapezium = 600 m²:
\[ \text{Area of a trapezium} = \frac{1}{2} \times h \times (a + b) \]
So,
\[ 600 = \frac{1}{2} \times 10 \times (25 + b) \]\
\[ 600 = 5 \times (25 + b) \]\
\[ 120 = 25 + b \]\
\[ b = 120 - 25 \]
\[ b = 95 \]
Hence the other parallel side of the trapezium is 95 m.