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Geometry Formulas You Need to Know: Triangles, Quadrilaterals, Nets, Prisms, & Composite Polygons

Learn the essential area and volume formulas for triangles, quadrilaterals, nets, prisms, and composite polygons. Understand how to find the area and volume of each shape step-by-step.

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Geometry Formulas You Need to Know: Triangles, Quadrilaterals, Nets, Prisms, & Composite Polygons

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  1. Triangles, Quadrilaterals, Nets, Prisms & Composite Polygons Finding Area & Volume

  2. Formulas You Need To Know PARALLELOGRAM TRIANGLE A = b x h A = b x h 2

  3. 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

  4. Finding Area - Triangles Area = b x h5 cm x 8 cm = 40 cm2 = 20 cm2 2 2 2 __________________________________________________ Area = b x h6 cm x 6 cm = 36 cm2 = 18 cm22 2 2 __________________________________________________ Area = b x h10 cm x 5 cm = 50 cm2= 25 cm2 2 22 4in

  5. Finding Area - Parallelograms A = b x h 10.3 cm x 6.2 cm = 63.86 cm2 _________________________________ A = b x h 10 cm x 3cm = 30 cm2 _________________________________ A = b x h 8 cm x 6 cm = 48 cm2

  6. Finding Area - Trapezoids • A = (b1 + b2) x h 1) 4 ft + 6 ft = 10 ft • 2 2) 10 ft x 2 ft = 20 ft2 3) 20 ft2 ÷ 2 = 10 ft2 _____________________________________________ A = (b1 + b2) x h 1) 2 ft + 4 ft = 6ft 2 2) 6ft x 5 ft = 30 ft2 3) 30 ft2 ÷ 2 = 15 ft2 _____________________________________________ A = (b1 + b2) x h 1) 7 ft + 8 ft = 15 ft 2 2) 15 ft x 4 ft = 60 ft2 3) 60 ft2 ÷ 2 = 30 ft2

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

  8. 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.

  9. Find the Area… Part A Part B Area of Part A: 1.7 cm x 4.9 cm = 8.33 cm2 Area of Part B: 2.1 cm x 1.3 cm = 2.73 cm2 The Composite Polygon’s Area is the total of the two parts: 8.33 cm2 + 2.73 cm2 = 11.06 cm2

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

  11. Finding Total Surface Area 1 5 2 6 4 3 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: 6 + 12 + 6 + 12 + 18 + 18 = 96 CM2

  12. FINDING VOLUME

  13. You Only Need One Formula Area of Base x Height of Prism Height of Prism The triangle is the BASE of the Prism

  14. 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

  15. 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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