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# Area of Complex Figures

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1. Area of Complex Figures

2. What are complex figures? Figures that can be subdivided into simple figures.

3. Subdivide this shape This shape can be subdivided into two rectangles.

4. Use what you know about rectangles to help you figure out missing sides. 28 cm. 12 cm. 25 cm. 13 cm. 13 cm. 12 cm. Since the side of this rectangle is 13; the other side has to be 13 also. Since we know the entire side of the figure is 25, subtract 13 from 25 to figure out the width of the red rectangle. 25 -13 = 12

5. Figuring out the area of complex figures 22 ft. 5 ft. 9 ft. 8ft. 4 ft. 14 ft. Step 1- Subdivide the figure into simple figures. Step 2- Figure out the missing measurements. Step 3- Calculate the area of both rectangles. Area = l x w Area = 14 x 9 Area = 126 Area = l x w Area = 8 x 5 Area = 40 Step 4- Add the areas of the simple figures together. 126 + 40 = 166 ft. 2

6. Let’s Give it a Try

7. Figuring out the area of complex figures 7 in. 5 in. 4 in. 4 in. 11 in. 15 in. Step 1- Subdivide the figure into simple figures. Step 2- Figure out the missing measurements. Step 3- Calculate the area of both rectangles. Area = l x w Area = 15 x 11 Area = 165 Area = l x w Area = 7 x 5 Area = 35 Step 4- Add the areas of the simple figures together. 165 + 35 = 200 in.2

8. Figuring out the area of complex figures 24 in. 2 in. 8 in. 19 in. 6 in. Step 1- Subdivide the figure into simple figures. 5 in. Step 2- Figure out the missing measurements. Step 3- Calculate the area of both rectangles. Area = l x w Area = 5 x 8 Area = 40 Area = l x w Area = 19 x 2 Area = 38 Step 4- Add the areas of the simple figures together. 40 + 38 = 78 in.2

9. Figuring out the area of complex figures 40 in. 7 in. 18 in. 24 in. 11 in. 11 in. 8 in. 8 in. Step 1- Subdivide the figure into simple figures. Step 2- Figure out the missing measurements. Step 3- Calculate the area of all the rectangles. Area = l x w Area = 8 x 18 Area = 144 Area = l x w Area = 24 x 7 Area = 168 Area = l x w Area = 8 x 18 Area = 144 Step 4- Add the areas of the simple figures together. 144 + 148 + 144 = 456 in.2

10. Figuring out the area of complex figures 12 in. 30 in. 30 in. 18 in. 30 in. Step 1- Subdivide the figure into simple figures. Step 2- Figure out the missing measurements. Step 3- Calculate the area of both polygons. Area = l x w Area = 18 x 30 Area = 540 Area = ½ bh Area = ½ 30 x 12 Area = 180 Step 4- Add the areas of the simple figures together. 540 + 180 = 720 in.2