5 Minute Check Find the area. Complete in your notes. 1. 2. 3. 4.

5 Minute Check Find the area. Complete in your notes. 1.

5 Minute Check Find the area. Complete in your notes. 1. A = 2u · 6u = 12u²

5 Minute Check Find the area. Complete in your notes. 2. A = 11.25 ·15.6 2 = 175.5 2 =87.75𝑚²

5 Minute Check Find the area. Complete in your notes. 2. A = 11.25 ·15.6 2 = 175.5 2 =87.75𝑚²

5 Minute Check Find the area. Complete in your notes. 3.

3. A = 10ft · 5ft = 50ft² 5 Minute Check Find the area. Complete in your notes. 3. A = 10ft · 5ft = 50ft²

5 Minute Check Find the area. Complete in your notes. 4.

5 Minute Check Find the area. Complete in your notes. . 4. A= 41.5 · 36 2 = 1494 2 =747 ft²

Lesson 9.6 Areas of Composite Figures Wednesday, March 29 Lesson 9.6 Areas of Composite Figures

Areas of Composite Figures Objective: To find areas of composite figures.

Area of Composite Figures A trapezoid is a quadrilateral with only one pair of parallel sides Parallel sides

Area of Composite Figures A composite figure is made up of two or more two dimensional shapes.

Area of Composite Figures Find the area of the figure. Can we divide the figure into a combination of rectangles and triangles?

Area of Composite Figures Find the area of the figure. Can we find the length of the base of the triangle? ?

Area of Composite Figures Find the area of the figure. Can we find the length of the base of the triangle? 12 – 5 = 7 7 in

Area of Composite Figures Find the area of the figure. What is the area of the rectangle? ? 7 in

Area of Composite Figures Find the area of the figure. What is the area of the rectangle? 5 · 7 = 35 in² What is the area of the triangle? 35 ? 7 in

Area of Composite Figures Find the area of the figure. What is the area of the rectangle? 5 · 7 = 35 in² What is the area of the triangle? 7 · 7 ÷ 2 = 24.5 in² What is the total area of the figure? 35 24.5 7 in

Area of Composite Figures Find the area of the figure. What is the total area of the figure? 35 in² + 24.5 in² = 59.5 in² 35 24.5 7 in

Area of Composite Figures Find the area of the figure. Since this is a trapezoid, we can use the trapezoid formula. A = h (𝒃₁+ 𝒃₂) 𝟐 First, add the top and bottom lengths

Area of Composite Figures Find the area of the figure. Since this is a trapezoid, we can use the trapezoid formula. A = h (𝟏𝟕) 𝟐 Then we divide by 2

Area of Composite Figures Find the area of the figure. Since this is a trapezoid, we can use the trapezoid formula. A = h (8.5) Then we multiply by the height

Area of Composite Figures Find the area of the figure. Since this is a trapezoid, we can use the trapezoid formula. A = 59.5in² Reminder – This only works with trapezoids, when b₁ and b₂ are parallel.

Area of Composite Figures Find the area of the figure. Do this on your own.

Area of Composite Figures Find the area of the figure. A = h (𝒃₁+ 𝒃₂) 𝟐 A = 4 (𝟐.𝟓+𝟒.𝟖) 𝟐 A = 4 · 3.65 A = 14.6 m²

Area of Composite Figures Find the area of the figure. Rectangle 2.5 · 4 = 10 m² Triangle 4 · 2.3 ÷ 2 = 4.6 m² Total Figure 10 m² + 4.6 m² = 14.6 m² 10 4.6 2.3 m

Area of Composite Figures Find the area of the figure. Do this on your own.

Area of Composite Figures Find the area of the figure. Rectangle 6 · 10 = 60 in² Triangle 4 · 4 ÷ 2 = 8 in² Total Figure 60 in² + 8 in² = 68 in² 8 4 in 60

Area of Composite Figures Find the area of the figure. Do this on your own. 10 m

Area of Composite Figures Find the area of the figure. A = h (𝒃₁+ 𝒃₂) 𝟐 A = 8 (𝟔+𝟏𝟏) 𝟐 A = 8 · 8.5 A = 68m² 10 m

Area of Composite Figures Find the area of the figure. Parallelogram 8 · 6 = 48 m² Triangle 5 · 8 ÷ 2 = 20 m² Total Figure 48 m² + 20 m²= 68 m² 10 m 48 20 5 m

Area of Composite Figures Find the area of the figure. Do this on your own. 4 in

Area of Composite Figures Find the area of the figure. Rectangle 4 · 12 = 48 ft² Triangle 4 · 6 ÷ 2 = 12 ft² Total Figure 48 ft² + 12 ft² = 60 ft² 6 ft 12 4 in 8 4 ft 48

Area of Composite Figures Find the area of the figure. Do this on your own. 4 in

Area of Composite Figures Find the area of the figure. A = h 𝟗𝒃₁+ 𝒃₂) 𝟐 A = 8( 𝟏𝟏+𝟏𝟒 𝟐 ) A = 8(12.5) A = 100 cm² 4 in

Area of Composite Figures Find the area of the figure. Parallelogram 8 · 11 = 88 cm² Triangle 3 · 8 ÷ 2 = 12 cm² Total Figure 88 cm² + 12 cm²= 100 cm² 4 in 88 12 3 cm

Area of Composite Figures Find the area of the figure. Do this on your own. 4 in

Area of Composite Figures Find the area of the figure. Rectangle 7 · 10 = 70 m² Triangle 2 · 3 ÷ 2 = 3 m² Total Figure 70 m² - 3 m² = 67 m² 2 m 3 3 m 4 in 70

Area of Composite Figures Find the area of the figure. Square 7 · 7 = 49 m² Trapezoid 3( 𝟓+𝟕 𝟐 ) = 18 m² Total Figure 49 m² + 18 m² = 67 m² 3 m 4 in 49

Area of Composite Figures Find the area of the figure. How to find the area of overlapping figures: Add the areas of the figures if they were not overlapped and then subtract the overlapped area.

Area of Composite Figures Find the area of the figure. What is the area of the square?

Area of Composite Figures Find the area of the figure. What is the area of the square? A = 12 ·12 = 144cm²

Area of Composite Figures Find the area of the figure. A = 12 ·12 = 144cm² What is the area of the rectangle?

Area of Composite Figures Find the area of the figure. A = 12 ·12 = 144cm² What is the area of the rectangle? A = 12 ·15 = 180cm²

Area of Composite Figures Find the area of the figure. A = 12 ·12 = 144cm² A = 12 ·15 = 180cm² What is the area of both figures?

Area of Composite Figures Find the area of the figure. A = 12 ·12 = 144cm² A = 12 ·15 = 180cm² What is the area of both figures? 144cm²+180cm²=324cm²

Area of Composite Figures Find the area of the figure. A = 324cm² What is the area of the overlapped area?

Area of Composite Figures Find the area of the figure. A = 324cm² What is the area of the overlapped area? A = 7 · 6 = 42cm² This is counted twice in the 324 cm²! 6 cm 7 cm

Area of Composite Figures Find the area of the figure. A = 324cm² A = 7 · 6 = 42cm² To find the total area, subtract the overlapped area from 324 cm². 6 cm 7 cm

Area of Composite Figures Find the area of the figure. A = 324cm² A = 7 · 6 = 42cm² What is the total area? 6 cm 7 cm

Area of Composite Figures Find the area of the figure. A = 324cm² A = 7 · 6 =42cm² What is the total area? 324cm² - 42cm² = 282cm²

Area of Composite Figures Find the area of the figure. This could have been divided into many rectangles. 42+42+42+96+60=282cm² 42cm² 60cm² 42cm² 96cm² 42cm²

Area of Composite Figures Find the area of the figure.

Area of Composite Figures Find the area of the figure. Area of the top rectangle A = 5 ·2 =10m² Area of the bottom rectangle. A = 3 ·2 = 6m² Overlapped area. A = 1 ·1 = 1m² Total area is 10m² + 6m² - 1m² = 15m² 1 m 1 m

Area of Composite Figures Find the area of the figure. Do this on your own.

Area of Composite Figures Find the area of the figure. Area of the top rectangle A = 6 ·7 =42ft² Area of the bottom rectangle. A = 6 ·8 = 48ft² Overlapped area. A = 5 ·5 = 25ft² Total area is 42ft² + 48ft² - 25ft² = 65ft² 5 ft 5 ft

Area of Composite Figures On the diagram, one square unit equals 10ft². Find the area of the figure.

Area of Composite Figures On the diagram, one square unit equals 10ft². Find the area of the figure. Full squares 30 · 10ft² = 300ft² Half squares 6 · 5ft² = 30ft² 300ft²+30ft²=330ft² 9 15 3 4 4 10 16 21 1 1 5 11 17 22 25 27 29 2 6 12 18 23 26 28 30 3 7 13 19 24 6 2 8 14 20 5

Area of Composite Figures Find the area of the figure.

Area of Composite Figures Find the area of the figure. Left Trap 5( 𝟏𝟎+𝟏𝟖 𝟐 ) = 70ft² Rectangle 20 · 18 = 360 ft² Right Trap 5( 𝟖+𝟏𝟖 𝟐 ) = 70ft² 360ft² + 70ft² + 70ft² = 500ft²

Area of Composite Figures Agenda Notes Homework– No Homework Mid-Chapter 9/10 Quiz –Friday, March 31

Area of Composite Figures Find the approximate area of Osceola County, Florida . Do this on your own.

Area of Composite Figures Find the approximate area of Osceola County, Florida . Rectangle 51 · 16 = 816 mi² Triangle 51 · 32 ÷ 2 = 816 mi² Total Figure 816 mi² + 816 mi² = 1632 mi² 32 mi

Area of Composite Figures Find the approximate area of Osceola County, Florida . A = h 9𝑏₁+ 𝑏₂) 2 A = 51( 16+48 2 ) A = 51(32) A = 1632 mi²

Area of Composite Figures Find the area of the figure.

Area of Composite Figures Find the area of the figure. Triangle 5 · 4 ÷ 2 = 10 cm² Rectangle 15 · 10 = 150 cm² Total Figure 150cm² + 10cm²= 160 cm²

Area of Composite Figures The picture shows one side a storage barn. What is the area of this side?

Area of Composite Figures The picture shows one side a storage barn. What is the area of this side? Area of the rectangle A = 14.5 · 22.8 = 330.6 ft² Area of the triangle A = 22.8(26.5−14.5 ) 2 =136.8 ft² Total area A = 330.6 ft² + 136.8 ft² = 467.4 ft²

Area of Composite Figures Find the area of the figure.

Area of Composite Figures Find the area of the figure. Rectangle 9 · 15 = 135 u² Top Triangle 6 · 9 ÷ 2 = 27 u² Bottom Triangle 6 · 3 ÷ 2 = 9 u² Total Figure 135 u² +27 u² - 9 u² = 153 u² 9 3

Air Review-No Calculator Dan buys a rug with an area of 49 6 square yards. The length is 7 3 yards. What is the width of the rug in yards?

Air Review-No Calculator Dan buys a rug with an area of 49 6 square yards. The length is 7 3 yards. What is the width of the rug in yards? 49 6 ÷ 7 3 49 6 · 3 7 21 6 3 1 2 yards

Air Review-No Calculator Dan buys a rug with an area of 49 6 square yards. The length is 7 3 yards. What is the width of the rug in yards? A = lh 49 6 = 7 3 · ? ? 7 2 = h 7 3 yards A = 49 6 yards² ? yards

Air Review-No Calculator 33.8 ÷ 32.5 =

Air Review-No Calculator 33.8 ÷ 32.5 = 1.04 1.04 325 )338.00 -325 1300 -1300 0