8. How is the area of a parallelogram found?
9. What is the altitude of a parallelogram whose base is 65 metres and area 1430 square metres?
10. How is a line divided when the sum of the squares on its segments is a minimum?
11. The area of a rectangle is 108.60 square metres and its perimeter is 48.20 linear metres; find its dimensions.
12. What Proposition in Book II. expresses the distributive law of multiplication?
13. On what proposition is the rule for extracting the square root founded?
14. Compare I. xlvii. and II. xii. and xiii.
15. If the sides of a triangle be expressed by x2 + 1, x2 − 1, and 2x linear units, respectively; prove that it is right-angled.
16. How would you construct a square whose area would be exactly an acre? Give a solution by I. xlvii.
17. What is meant by incommensurable lines? Give an example from Book II.