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**Triangles, Quadrilaterals, Nets, Prisms & Composite Polygons**

Finding Area & Volume

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**Formulas You Need To Know**

PARALLELOGRAM TRIANGLE A = b x h A = b x h 2

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**Formulas You Need To Know**

TRAPEZOID 1) add the top & bottom bases 2) multiply the sum by height 3) divide by 2 A = (b1 + b2) x h 2

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**Finding Area - Triangles**

Area = b x h 5 cm x 8 cm = 40 cm2 = 20 cm __________________________________________________ Area = b x h 6 cm x 6 cm = 36 cm2 = 18 cm Area = b x h 10 cm x 5 cm = 50 cm2 = 25 cm 4in

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**Finding Area - Parallelograms**

A = b x h cm x 6.2 cm = cm2 _________________________________ A = b x h cm x 3 cm = 30 cm2 A = b x h cm x 6 cm = 48 cm2

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**Finding Area - Trapezoids**

A = (b1 + b2) x h ) 4 ft + 6 ft = 10 ft ) 10 ft x 2 ft = 20 ft2 3) 20 ft2 ÷ 2 = 10 ft2 _____________________________________________ A = (b1 + b2) x h ) 2 ft + 4 ft = 6 ft ) 6 ft x 5 ft = 30 ft2 3) 30 ft2 ÷ 2 = 15 ft2 A = (b1 + b2) x h ) 7 ft + 8 ft = 15 ft ) 15 ft x 4 ft = 60 ft2 3) 60 ft2 ÷ 2 = 30 ft2

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Composite Polygons A Composite Polygon is an irregular polygon made up of different polygons. To find the AREA OF A COMPOSITE POLYGON, first break the polygon into simpler parts.

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**Finding Area – Composite Polygon**

This shape breaks down into these two shapes. So… find the area of each of the two areas separately and add the areas together.

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**Find the Area… Area of Part A: 1.7 cm x 4.9 cm = 8.33 cm2**

Part B Area of Part A: cm x 4.9 cm = 8.33 cm2 Area of Part B: cm x 1.3 cm = 2.73 cm2 The Composite Polygon’s Area is the total of the two parts: 8.33 cm cm2 = cm2

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**Net Figures – Total Surface Area**

Total Surface Area Find the area of each shape separately, then add the areas together.

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**Finding Total Surface Area**

1 3 2 4 5 6 AREA OF RECTANGLE 1: 3 CM X 2 CM = 6 CM2 AREA OF RECTANGLE 2: 6 CM X 2 CM = 12 CM2 AREA OF RECTANGLE 3: 3 CM X 2 CM = 6 CM2 AREA OF RECTANGLE 4: 6 CM X 2 CM = 12 CM2 AREA OF RECTANGLE 5: 3 CM X 6 CM = 18 CM2 AREA OF RECTANGLE 6: 3 CM X 6 CM = 18 CM2 TOTAL SURFACE AREA: = 96 CM2

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FINDING VOLUME

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**You Only Need One Formula**

Area of Base x Height of Prism The triangle is the BASE of the Prism Height of Prism

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**area of base x height of prism**

Follow These Steps… Identify the shape of the base: Triangle 2) What is the formula for area for that shape: (b x h) / 2 3) What is the area of the base: (7 x 8) / 2 = 56/2 = 28 4) What is the height of the prism: 13 5) What is the formula for volume: area of base x height of prism 6) What is the volume of the prism: 28 x 13 = 364

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Follow These Steps… Identify the shape of the base: Square 2) What is the formula for area for that shape: b x h 3) What is the area of the base: 3 cm x 5 cm = 15 cm2 4) What is the height of the prism: 4 cm 5) What is the formula for volume: area of base x height of prism 6) What is the volume of the prism: 15 cm2 x 4 cm = 60 cm3

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