2. The difference in time between two places is 3 hr. What is their difference in longitude?

16 min. 23 sec.

3. The difference in time between Boston and New Orleans is 1 hr. 16 min. 14 sec. What is their difference in longitude?

4. The difference in time between New York and St. Louis is 1 hr. 2 min. 20 sec. What is the difference in their longitude?

5. Two persons observed the occultation of a certain star by the moon, one seeing it at 9 P.M., and the other at 101 P.M. What was the difference in their longitude?

6. The difference in time between Savannah, Ga., and Portland, Me., is 43 min. 32 sec. What is their difference

in longitude?

7. The difference in time between London and New York is 4 hr. 55 min. 37 sec. What is their difference in longitude?

8. When it is 12 o'clock M. at Rochester, N.Y., it is 9 hr. 1 min. 47 sec. A.M. at San Francisco. The longitude of Rochester is 77° 51' west from Greenwich. What is the longitude of San Francisco?

9. When it is noon at Greenwich it is 6 hr. 52 min. 40 sec. A.M. at Harrisburg, Penn. What is the longitude of Harrisburg?

10. A traveler found on arriving at his destination that his watch was 1 hr. 35 min. too slow. In which direction had he been traveling? How far had he traveled?

11. When it is noon at Philadelphia it is 10 min. past 5 o'clock P.M. at Paris. What is the longitude of Paris, the longitude of Philadelphia being 75° 10' ?

PRACTICAL MEASUREMENTS.

242. The method of computing the area of a rectangle and a square was learned in Art. 214, but there are other surfaces whose area can be readily found.

243. When a straight line meets another straight line forming two equal angles, each angle is called a Right Angle.

When two lines form right angles, they are said to be perpendicular to each other.

244. An angle smaller than a right angle is called an Acute Angle.

245. An angle larger than a right angle is called an Obtuse Angle.

246. Lines which are equidistant throughout their entire length are called Parallel Lines.

247. A figure having four straight sides and its opposite sides parallel is called a Parallelogram.

1. When the angles of a parallelogram are right angles, it is called a Rectangle.

2. The side upon which a figure is assumed to stand is called the Base.

3. The perpendicular distance between the base of a figure and the highest point opposite it is the Altitude.

4. The straight line joining the opposite angles of a parallelogram is called its Diagonal.

Altitude

Two Right Angles

Acute Angle

Obtuse Angle

Parallel Lines

Parallelogram

Rectangle

Diagonal

WRITTEN EXERCISES.

248. The measurement of rectangles. (See § 214.)

Find the area of a rectangular figure

9. A gable roof was 43 ft. by 26.

feet of tin will be required to cover it?

How many square

10. A lot was 18 rods long and 8 rods wide. What part of an acre did it contain?

11. What was the value of the above lot at $342.50 per acre?

12. How many acres are there in a square farm, each of whose sides is 20 chains?

13. A rectangular piece of land is 160 rods long and 120 rods wide. How many acres does it contain?

14. A man bought a rectangular farm 40 ch. long and 35 ch. wide, at $85 an acre. What did the farm cost? 15. The area of a certain rectangular garden is 840 square yards, and its length is 35 yards. How wide is it?

16. A rectangular field containing 8 acres is 32 rods wide. How long is it?

17. A rectangular mirror has an area of 2520 sq. in. If its width is 3 ft., what is its length?

18. A city lot containing 1610 sq. yd. has a front of 80 ft. What is its depth?

19. A rectangular farm containing 100 acres is 80 rods wide. How long is it?

249. The measurement of parallelograms.

It is apparent that the parallelogram ABCD = the rectangle EFCD; that the base AB = the base EF, and that the altitude of each is DE. Hence a parallelogram is equivalent to a rectangle having the same base and altitude.

250. PRINCIPLE.

The area of a parallelogram is equal

to the product of the numbers expressing its base and altitude. The base and altitude must be expressed in units of the same denomination.

9. The area of a parallelogram is 1628 sq. ft. Its length is 74 ft.

What is its altitude?

10. The area of a parallelogram is 3404 sq. ft. It has an altitude of 37 feet. What is its length?

11. I have a lot in the form of a parallelogram containing one acre. The distance between two of its parallel sides

is 12 rods. What is its length?

12. The area of a field is 31 acres.

It is in the form of

a parallelogram, and its length is 80 rods. How wide is it? 13. There is a farm in the form of a parallelogram containing 132 acres. The perpendicular distance between the What is its length?

sides is 132 rods.

251. To find the area of a triangle.

252. A figure having three sides and three angles is called a Triangle.

The point where the sides which form an angle meet is called the Vertex.

Altitude

Base

We have just learned that the area of a parallelogram is equal to the product of the numbers expressing its base and altitude. It is evident that a diagonal of a parallelogram divides it into two equal triangles. Hence,

253. PRINCIPLE.

The area of a triangle is one half the

product of the numbers expressing its base and altitude.

6.

Base 40 ft., alt. 25 ft.

3. Base 37 ft., alt. 28 ft. 7. The base of a triangular field is 360 yards, and the altitude is 615 feet. How many acres does it contain?

8. What will be the cost of a triangular piece of land whose base is 18.36 ch., and the altitude 10.54 ch., at $70 per acre?

9. How many square feet of boards will be required to cover the gables of a house that is 28 ft. wide, the ridge of the roof of the house being 13 ft. higher than the foot of the rafters ?

254. To find the area of a trapezoid.

255. A figure having four sides, two of which are parallel, is called a Trapezoid.

B

It is evident that any trapezoid may be divided into two triangles by a line; as, AC. The area of one triangle is the product of one half the length of one of the parallel sides, as AD, multiplied by the altitude CE, and the area of the other triangle is the product of one half the length of the other parallel side, as CB, multiplied by the altitude CE. Therefore,

Altitude

A Trapezoid E