Unit 11 Area of Polygons and the Coordinate Plane
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1 Unit 11 Area of Polygons and the Coordinate Plane Date Target Assignment Done! W a 11.1a Worksheet R b 11.1b Worksheet F c 11.1c Day 1 Worksheet M c 11.1c Day 2 Worksheet T 3-15 Quiz Quiz 11.1 W Worksheet R Day 1 Worksheet F Day 2 Worksheet M 3-21 Review Review Worksheet T 3-22 Quiz Quiz W 3-23 Review Unit 11 Test Review Worksheet R 3-24 Test Unit 11 Test ENJOY YOUR SPRING BREAK!!! Target 11.1: Determine and calculate area of triangles, quadrilaterals, and regular polygons 11.1a: Area of Triangles and Parallelograms 11.1b: Area of Trapezoids, Rhombuses, and Kites 11.1c: Area of Regular Polygons Target 11.2: Use the coordinate plane to classify the quadrilateral Target 11.3: Using the coordinate plane, calculate the perimeter and area of the figure Name:
2 11.1a - Areas of Triangles and Parallelograms Target 1: Determine and calculate area of triangles, quadrilaterals, and regular polygons Vocabulary: Draw and take notes here Area of a Square The area of a square is the of the length of its side. What is the formula to find the area of a square? Area of a Parallelogram The area of a parallelogram is the product of a and its cooresponding. Example 1: Use a formula to find area Find the area of parallelogram ABCD Area of a Triangle The area of a triangle is the product of a and its corresponding. Example 2: Solve for unknown measures The base of a triangle is four times its height. The area of the triangle is 50 square inches. Find the base and height.
3 Area Addition Postulate The area of a region is the of the areas of its nonoverlapping parts. Example 3: Solve a multi-step problem Vacuum A robotic vacuum cleaner can clean 2 square meters of carpet in 8 minutes. About how long does it take for it to clean a carpet covering a room with the dimensions on the right? Write down two questions that you have. 1) 2) YOU TRY NOW! 1. A parallelogram has an area of 133 square feet and a height of 19 feet. What is the length of the base?
4 11.1b Area of Trapezoids, Rhombuses, and Kites Target 1: Determine and calculate area of triangles, quadrilaterals, and regular polygons Vocabulary: Height of a trapezoid: Area of a Trapezoid The area of a trapezoid is one half the product of the height and the sum of the lengths of the bases. Example 1: Find the area of a trapezoid Beavers To prevent beavers from damming a drainage pipe, the trapezoid-shaped fence shown is placed at the pipe. Approximate the area of the enclosed fence. Area of a Rhombus The area of a rhombus is one half the product of the lengths of the diagonals Draw here
5 Area of a Kite The area of a kite is one half the product of the lengths of the diagonals Draw here Example 2: Find the area of a rhombus Find the area of the rhombus YOU TRY NOW! Find the area of the figure What is the distance formula? 3. Find the area of a rhombus with vertices M(2, 4), N (5, 6), P(8, 4), and Q (5, 2).
6 11.1c Areas of Regular Polygons Target 1: Determine and calculate area of triangles, quadrilaterals, and regular polygons Vocabulary: Center of a Polygon: Radius of a Polygon: Label Me! Apothem of a Polygon: Central Angle of a Regular Polygon: Example 1: Find angle measures in a regular polygon In the diagram, ABCDEF is a regular hexagon in G. Find each angle measure. a. m EGF b. m EGH c. m HEG Area of a Regular Polygon The area of a regular with side lengths is half the the product of the apothem and the perimeter. What are the two properties that make
7 Example 2: Find the area of a regular polygon Coaster A wooden coaster is regular octagon with 3-centimeter sides and radius of about 3.92 centimeters. What is the area of the coaster? YOU TRY NOW! 1. In the diagram, FGHJ is a square inscribed in K. Find m FKJ and m KJF. 2. The radius of the regular pentagon is about 6.8 inches. Find the area of the to the nearest square inch.
8 11.2 Determine the Type of Quadrilateral Using the Coordinate Plane Target 2: Use the coordinate plane to classify the quadrilateral YOUTUBE VIDEO: Determine a quadrilateral with coordinate geometry Example 1: Using Coordinate Geometry to classify the type of polygon Given the quadrilateral ABCD with A (-4, 1), B(-2, 4), C (4, 0), and D (2, -3). What shape is ABCD? Prove it. Show all work and explain your choice. Find the point where the diagonals intersect. YOU TRY NOW! Quadrilateral ABCD with A (4, 7), B(9, 7), C (6, 3), and D (1, 3). What shape is ABCD? Prove it. Show all work and explain your choice. Find the point where the diagonals intersect.
9 11.3 Find the Perimeter and Area of a Figure Target 3: Using the coordinate plane, calculate the perimeter and area of the figure YOUTUBE VIDEO: area and perimeter of polygons in a coordinate plane Example 1: Draw and classify the polygon with the given vertices. Find the perimeter and area. F (2, 8), G(4, 4), H (2, 0) Example 2: Find the area of the polygon with vertices L (3, 5), M (6, 8), N(9, 6), P (5, 0) What is the Pythagorean Theorem?
10 YOU TRY NOW! Find the perimeter area of of ABCD with vertices A(-3, 0), B(3, 2), C(4, -1) and D(-2, -3)
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