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Calculating the Area of Combined Figures: A Step-by-Step Guide

In this lesson, we explore how to calculate the area of complex figures by breaking them down into familiar shapes such as rectangles, triangles, or circles. Through practical examples like a dining room floor plan and a park sketch, we demonstrate strategies for dividing figures and using area formulas provided on the NJ Ask Reference Sheet. Learn how to effectively determine the total area by calculating each segment and adding them together, ensuring accurate results for various real-world applications.

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Calculating the Area of Combined Figures: A Step-by-Step Guide

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  1. Lesson 29 Area of a Combined Figure

  2. Get the Idea • Sometimes, you need to find the area of a figure that is not a common shape. You can often do this by dividing that figure into familiar shapes, such as triangles, rectangles or circles. • The formulas for finding the area of triangles, rectangles or circles will be provided for you on the NJAsk Reference Sheet

  3. Example 1 • This is the floor plan of the dining room n a new house. The dining room is rectangular with another rectangular area near one end. How many square feet of wood flooring would be needed to completely cover the floor in this room? 12 ft 15 ft 12 ft 18 ft

  4. Strategy • Divide the figure into two shapes. Then find the area of each. • 12 x 12= 144 and 6x15= 90. 144+90= 234 sq.ft 12 ft 15 ft 6x15 12 ft 12x12 12 ft 6ft Total: 18 ft

  5. Example 2 • This is a sketch of a park near McHenry School. Find the area of the park. • How would I cut this shape up? 30 ft 50 ft 50 ft 50 ft

  6. How we cut it up… • Divide the figure into two shapes. Then find the area of each. • Square: 50x50= 2500 • Triangle: ½(50x30)= ½ (1500)= 750 • 2500+750 = 3250 sq ft. ½(50 x30) 50 ft 30 ft 50 x50 50 ft 50 ft

  7. One more together • What is the total area of the figure below? • Draw a line to divide the figure above into a ¼ circle and a square. • How do I find the area of a ¼ circle? • What do I do to find the total area of the shape? 10m 10m 10m

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