Geometry Q3 Review
Additional topics: Constructions and midpoint
1. If W(-4, -5), X(1, 0), Y(-1, 2) and Z(-6, -3), what shape is WXYZ? Prove your answer!
2. Find the sum of the interior angles of a 7-gon.
3. Find the size of each of the exterior angles of a regular 17-gon.
4. Find the size of each of the interior angles of a regular 12-gon.
5. Each angle of a regular n-gon measures 156°. How many sides does this n-gon have?
6. Each angles of a regular n-gon measure 165.6°. How many sides does this n-gon have?
7. Find the area of a regular pentagon with side length 8 cm.
8. Find the area of a regular decagon with side length 14 in.
9. Using the pentagon at right, write and solve and equation for x.
10. Each exterior angle of a regular polygon measure 22.5°. How
many sides does the polygon have?
5
11. If figure A and figure B are similar with a ratio of similarity of , and the perimeter of figure
4
A is 18 units, what is the perimeter of figure B?
1
12. If figure A and figure B are similar with a ratios of similarity of , and the area of figure A is
8
13 square units, what is the area of figure B?
23
13. If figure A and figure B are similar and the ratio of their perimeters is , does that mean
11
the perimeter of figure A is 23 units and the perimeter of figure B is 11 units? Explain.
14. Find the length of the radius. The shaded area is 12π sq cm. The entire sector is shaded.
15. Find the area of each shaded region.
a.
b.
16. Find the area of the shaded sector. Then find the arc length of
the shaded sector.
17. Kennedy and Tess are constructing a racetrack for their horses.
The track encloses a field that is rectangular, with two semicircles at
each end. A fence must surround this field. How much fencing will they need?
18. Two rectangular prisms are similar. The smaller, A, has a height of 4 units while the larger,
B, has a height of 6 units.
a. What is the scale factor from prism A to prism B?
b. What is the ratio of the lengths of the edges labeled x and y?
c. What is the ratio of their surface areas?
d. What is the ratio of their volumes?
e. A third prism C is similar to prisms A and B. Prism C’s height is
10 units. If the volume of prism A is 25 cubic units, what is the
volume of prism C?
19. Find the volume.
a.
b.
20. Solve for a and b.
Answers:
1. The slopes are: WX = 1, XY = -1, YZ = 1, and ZW = -1. This shows that WXYZ is a rectangle.
2. 900°
3. 21.1765°
4. 150°
5. 15 sides
6. 25 sides
2
2
7. 110.1106 cm
8. 1508.0649 cm
9. X ≈ 28.05
10. 16 sides
11. 14.4 units
12. 832 sq units
13. No, it just tells us the ratio. Figure A could have a perimeter of 46 units while figure B has
a perimeter of 22 units.
14. 6 cm
15 a. 196 - 49π sq ft.; b. 10π sq in.
16. 2π sq un; π units
17. 2816 + 302π ≈ 3764.76 meters of fencing
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18. a. ; b. ; c. ; d. ; e. 390.625 cu units.
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19. a. 336π cubic un ; b. 90π cubic in.
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20. a = 64°, b = 138 °
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