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. G FD 2)Given: DF = 7x + 5, FG = 12x + 8, and.

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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. G FD 2)Given: DF = 7x + 5, FG = 12x + 8, and DG = 30x + 2. Find x, DF, FG and DG. G H F 3)Given: m  EFG = 4x, m  GFH = 8x, and m  EFH = 14x – 22. Solve for x and the measure of each angle. E

Lateral Edge is not necessarily the altitude. Base Altitude (height) Lateral Face Lateral Edges

6ft 4ft 10ft Lateral Area – sum of the areas of the lateral faces Left side = ________ Right side = ________ Front = ________ Back = ________ 6·4 = 10·6 = L.A. = 168 ft² Theorem 11-1

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

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

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

6cm8cm 18cm Find the L.A. and the T.A. 6² + 8² = x² L.A. = ( )(18) L.A. = 432 cm² T.A. = L.A. + 2B = (½6·8) T.A. = 480 cm² 6cm 8cm 10cm

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

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

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

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

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