Calculating the Area of Polygons
Calculating the Area of Polygons is a skill on Pengi from Lesson 4: Polygons in Illustrative Mathematics, Grade 6.
Key Concepts
Property The area of a polygon on a coordinate plane can be found using two common methods: 1. Decomposition: The polygon is divided into smaller, non overlapping shapes like triangles and rectangles. The total area is the sum of the areas of these smaller shapes. $$A {polygon} = A {shape1} + A {shape2} + \dots$$ 2. Enclosure (Box Method): A rectangle is drawn to enclose the entire polygon. The area of the polygon is the area of the rectangle minus the areas of the regions outside the polygon but inside the rectangle. $$A {polygon} = A {rectangle} A {outside\ regions}$$.
Examples Decomposition Method: To find the area of the polygon, we can decompose it into a trapezoid and a smaller triangle. The trapezoid has area 9 square units, and the small triangle has area 3 square units. Adding them together, the total area is ($A = 9 + 3 = 12$) square units.
Enclosure Method: To find the area of the polygon, we can enclose the polygon in a rectangle with area 20 square units, then subtract the areas of three right triangles outside the polygon, which are 6, 3, and 2.5 square units. The total area is ($A = 20 (6 + 3 + 2.5) = 8.5$) square units.
Common Questions
What is Calculating the Area of Polygons?
Calculating the Area of Polygons is a skill on Pengi from Lesson 4: Polygons in Illustrative Mathematics, Grade 6.
What grade level is Calculating the Area of Polygons for?
Calculating the Area of Polygons is part of the Grade 6 Math curriculum, covered in Illustrative Mathematics, Grade 6. It is designed for students studying Math at the Grade 6 level.
How can I learn Calculating the Area of Polygons?
Pengi offers an AI-guided lesson for Calculating the Area of Polygons that walks you through the key concepts step by step. The lesson is aligned to Illustrative Mathematics, Grade 6 so the content matches what you see in class.
How do I practice Calculating the Area of Polygons?
After learning the concept, use the Practice mode to work through targeted exercises on Calculating the Area of Polygons. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Calculating the Area of Polygons?
Calculating the Area of Polygons is covered in Illustrative Mathematics, Grade 6, specifically in Unit 1 Area and Surface Area under Lesson 4: Polygons. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Calculating the Area of Polygons free to study on Pengi?
Yes, the core Learn and Practice modes for Calculating the Area of Polygons are available for free on Pengi. No credit card is required to start studying.