1. 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

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

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

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

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 = 324 + 2(9 · 9) T.A. = 324 + 162 =486 m²

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

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

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

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

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

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. 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)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

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