Geo_Book_Answers

Answers to Exercises
LESSON 8.4
1. 2092 cm2 2. 74 cm
3. 256 cm 4. 33 cm2 5. 63 cm 6. 490 cm2 7. 57.6 m 8. 25 ft
9. 42 cm2 10. 58 cm2 11. a 1
2 s; A 1
2 asn 1
2 1
2 s s 4 s2 12. It is impossible to increase its area, because a
regular pentagon maximizes the area. Any
dragging of the vertices decreases the area.
(Subsequent dragging to space them out more
evenly can increase the area again, but never
beyond that of the regular pentagon.)
13. 996 cm2 14. 497 cm2 15. total surface area 13,680 in2 95 ft2 ;
cost $8075
16. Area is 20 square units.
y
y
1_
2
x 5
(2, 6)
y 2x 10
100 ANSWERS TO EXERCISES
x
17. Area is 36 square units.
y
y –
4_ x 12
3
(6, 4)
18. Conjecture: The three medians of a triangle
divide the triangle into six triangles of equal area.
Argument: Triangles 1 and 2 have equal area
because they have equal bases and the same
height. Because the centroid divides each median
into thirds, you can show that the height of
triangles 1 and 2 is 1
3 the height of the whole
triangle. Each has an area 1
6
the area of the whole
triangle. By the same argument, the other small
triangles also have areas 1
6 the area of the whole
triangle.
1
h
y –
1_ x 6
3
19. nw ny 2x
20. 504 cm 2
21. 840 cm 2
2
x