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10:3 Area of Parallelograms Objective: Find the area of parallelograms and composite figures Standard: G4.2 Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures. RELEVENCE: Area of parallelograms is used in construction and interior design. PRIOR LEARNING: Area of basic figures is learned in elementary school. Perimeter of Squares & Rectangles Square EXAMPLE: Find the perimeter. P = 4s Rectangle 20cm P = 2l + 2w P – Perimeter 14cm 12cm s – side l – length w – width Area of Square & Rectangle Square EXAMPLE: Find the area. A = s2 Rectangle 20cm A = l ◦ w A – area 14cm 12cm s – side l – length w – width Base: ANY side of a parallelogram can be called a base For each base, there is a corresponding altitude Altitude: A corresponding altitude is any segment perpendicular to the base Thelength of an altitude is called the height of the parallelogram Perimeter of Parallelograms: P=add all sides EXAMPLE: Find the perimeter. (do not use height) P – perimeter 14cm 20cm 12cm Area of Parallelograms: A = bh EXAMPLE: Find the area. A – area b – base 14cm 20cm h - height 12cm Postulate: Thearea of a region is the sum of the areas of all of its non-overlapping parts. Example 1: Find the area of the figure. 7 ft 12 ft 5 ft 17 ft Example 2: Find the area of the figure. 9 cm 3 cm 7 cm 9 cm 4 cm 13 cm Example 3: Real-world Application Taylor’s grandparents are moving into a retirement home. Bedroom Bath 2 Before they move in, Bedroom 12 ft 17 ft 1 they want to recarpet 20 ft 5 ft Hall the two bedrooms 20 ft and hall. Find the 14 ft amount of carpeting needed to cover this floor space. YOUR TURN: Find the area of each figure. 1. 4mm 2. 15 in. 6 in. 8mm 5 in. 6mm 6 in. 2 in. 16 in. 10mm A – B Pair Share 1. Person “A” works the first problem while person “B” observes and coaches when necessary. 2. When “A” finishes, “B” is to initial the problem to show agreement with the results. 3. “A” and “B” switch roles and repeat steps 1 and 2. EXIT TICKET Show your work! Youmay use your notes but DO NOT help each other!
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