PROBLEM I. Plate 5. fig. 70.
To find the area of a square.

RULE.

Multiply the fide by itself, and the product will be the area.

EXAMPLE I.

How many square yards are in a square, whose fide is 15 feet?

Ex. 2. Required the area of a square, whose side is 12 feet? Ans. 144 square feet. Ex. 3. How many square feet are in a square, whose side is 6 feet 3 inches ? Anf. 39 feet o in. 9 pts. Ex. 4. How many square yards are in a square court, whose fide is 80 feet? Anf. 715 yds. 5 feet o in. 9 pts. Ex. 5. How many square chains are in a field, whose side is mile? Ans. 6400 fq. chains.

Ex. 6. Required the area of a square, whose fide is 3 chains?

PROBLEM II. Plate 5. fig. 71.

To find the area of a rectangle.

RULE.

Anf. 9 fq. ch.

Multiply the length by the breadth, and the product is the

area.

EXAMPLE İ.

Required the area of a rectangle, whose height is 3000 links, and breadth 1670 links of the English chain.

1670

3000

50,10000 square links.

4

40000

40

16,00000

Ans. 50 acres, o roods 16 poles.

Here

Here, because the chain is divided into 100 links, and that 100 X 100 is 10000 (the number of square links in one square chain) and 10000 × 10 = 100000 (the number of square links in one acre) divide the product by 100000, the quot gives acres and decimals of an acre; and this decimal is reduced to value by multiplying by 4, by 40, by 304. Or, instead of dividing the square links by 100000, cut off five decimal places towards the right hand, the integral part gives acres, and those cut off are decimals of an acre, and are reduced to value accordingly. Ex. 2. Required the area of a rectangular field, whose fides are 5.5 and 2.54 Scots chains.]

Ans. 1 acre I rood 2.3 falls 18.72 ells. Ex. 3. Required the area of a rectangle, whose length is 15 feet, and breadth 12 feet. Anf. 186 square feet. Ex 4. Required the area of a rectangle, whose length is 10 Anf. 60 inches.

inches, and breadth 6 inches.

Ex. 5. Required the area of a rectangle, whose fides are 56 Anf. 1036 square feet.

feet, and 18 feet 6 inches?

Ex. 6. Required the area of a rectangle, whose length is 16+,

and breadth 10 yards

Anf. 168.3 yds.

PROBLEM III. Plate 5. fig. 72

To find the area of a rhombus or rhomboid.

RULE.

Multiply the length by the perpendicular breadth, and the product is the area.

EXAMPLE I.

Required the area of a rhombus, whose side is 750 links, and

one of its acute angles 60°.

When one of the angles of a rhombus or rhomboid are gi

ven, the area may be found by the following proportion.

As rad: fine included ang. :: the prod. containing fides: area.

Ans. 4 acres 3 roods 19 falls 13 ells nearly.