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Given: DF = 7x + 5, FG = 12x + 8, and DG = 30x + 2. Find x, DF, FG and DG.

WARM UP. 1) If two supplementary angles are mA = 4x + 31 and mB = 2x – 7, solve for x and find mA and mB. Given: DF = 7x + 5, FG = 12x + 8, and DG = 30x + 2. Find x, DF, FG and DG. D. F. G. G.

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Given: DF = 7x + 5, FG = 12x + 8, and DG = 30x + 2. Find x, DF, FG and DG.

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  1. WARM UP 1) If two supplementary angles are mA = 4x + 31 and mB = 2x – 7, solve for x and find mA and mB. • Given: DF = 7x + 5, FG = 12x + 8, and DG = 30x + 2. Find x, DF, FG and DG. D F G G • Given: mÐEFG = 4x, mÐGFH = 8x, and mÐEFH = 14x – 22. Solve for x and the measure of each angle. E F H

  2. Section 12-1 Prisms

  3. Rectangular Prism – A three dimensional object with two rectangular bases and four rectangular lateral faces. Base (B) Base (B) Right Left Front Back

  4. Lateral Area – sum of the areas of the lateral faces 6ft 4ft 10ft 6·4 = 24 Left side = ________ Right side = ________ 6·4 = 24 L.A. = 168 ft² Front = ________ 10·6 = 60 Back = ________ 10·6 = 60

  5. Lateral Area can also be found by taking the perimeter of the base times the height. 6ft L.A. = ph 4ft 10ft L.A. = (10 + 4 + 10 + 4)(6) L.A. = (28)(6) L.A. = 168 ft²

  6. Total Area (aka Surface Area) Lateral Area + Area of the Bases T.A. = L.A. + 2B L.A. = (9·4)(9) = (36)(9) 9m L.A. = 324 m² T.A. = L.A. + 2B 9m = 324 + 2(9·9) 9m T.A. = 324 + 162 = 486 m²

  7. These formulas will work for all types of prisms. Prisms are named for their bases: Hexagonal Prism Rectangular Prism Triangular Prism

  8. Find the L.A. and the T.A. 8cm 6cm 6cm 8cm 10cm 6² + 8² = x² L.A. = (6 + 8 + 10)(18) 18cm L.A. = 432 cm² T.A. = L.A. + 2B = 432 + 2(½6·8) T.A. = 480 cm²

  9. Find the L.A. and the T.A. 30º 6 14in. 60º 3 6in. A = ½ap = ½( )(36) = 6in. T.A. = L.A. + 2B L.A. = (6·6)(14) T.A. = 504 + 2( ) L.A. = 504 in²

  10. Volume – area of the base times the height V = Bh area of the base Measured in cubic units (in³, cm³, ft³)

  11. Find the L.A. T.A. and Volume 7ft 2ft 11ft T.A. = L.A. + 2B L.A. = (26)(7) = 182 + 2(11·2) L.A. = 182 ft² T.A. = 226 ft² V = Bh V = (22)(7) V = 154 ft³

  12. Section 12-3 Cylinders

  13. Cylinders – Cylinders are very similar to the prisms that we have been examining. The only difference is that instead of polygons (rectangle, triangle, trapezoid, hexagon) as bases, a cylinder has circular bases. The formulas to calculate lateral area, total area, and volume will be nearly the same as prisms.

  14. Cylinders L.A. = (p)h L.A. = (2πr)h T.A. = L.A. + 2B T.A. = 2πrh + 2(πr²) V = Bh V = (πr²)h

  15. Find the L.A. T.A. and Volume 20in. 5in. L.A. = (2πr)h T.A. = 2πrh + 2(πr²) V = (πr²)h T.A. = 200π+ 2(π·5²) V = (π·5²)(20) L.A. = (2π·5)(20) T.A. = 200π + 50π V = 500π in³ L.A. = 200π in² T.A. = 250π in²

  16. Find the L.A. T.A. and Volume 10in 4in L.A. = (2πr)h T.A. = 2πrh + 2(πr²) V = (πr²)h T.A. = 80π+ 2(π·4²) V = (π·4²)(10) L.A. = (2π·4)(10) T.A. = 80π + 32π V = 160π in³ L.A. = 80π in² T.A. = 112π in²

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