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the room, the height of the room, and the total wall-surface respectively. Hence the rule.

Ex. How many sq. ft. of paper will be required for a room 16 ft. by 12 ft. and 8 ft. in height, and what will it cost at 18. 6d. per. sq. yd.?

Distance round the room=16+12+16+12=56 ft.

Area of wall-surface

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=56×8=448 sq. ft.

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1s. 6d.÷9=2d.

=2d. x 448=896d. =74s. 8d.
= £3 14s. 8d.

55. Deductions must be made for doors, fireplaces, windows, and cupboards. From the total area of the wall-surface, subtract the total area of the doors, etc.; and the remainder will be the area of the surface to be papered, plastered, or painted, as the case may be.

Ex. What is the cost of painting the walls of a room, 20 ft. long, 16 ft. broad, and 10 ft. high, at 9d. per sq. yd., allowing for a doorway 6 ft. 6 in. x 4 ft., 2 windows each 4 ft. 6 in. x 4 ft., and a fireplace 5 ft. square?

Circuit of room=72 ft.

Total area of wall-surface

Area of doorway

Area of windows

Area of fireplace

=6

72 ft. x 10 ft. =720 sq. ft.

ft. x 4 ft. =26 sq. ft.
4 ft. x 4 ft. x2=36 sq. ft.
=5 ft. x 5 ft.=25 sq. ft.

=

Total area to be deducted=26 sq. ft.+36 sq. ft.+25 sq. ft.

Total area to be painted

=87 sq. ft.

=720 sq. ft.-87 sq. ft.
= 633 sq. ft.

=

Cost of painting per sq. ft. =9d.÷9=1d.

Total cost of painting

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Find the number of square feet of wall-paper required for rooms whose dimensions are as follows:

(1) Length, 18 ft.; breadth, 16 ft.; height, 10 ft.

(2) Length, 15 ft.; breadth, 8 ft.; height, 9 ft.

(3) Length, 16 ft. 6 in.; breadth, 15 ft. 9 in.; height, 8 ft. 6 in. (4) Length, 20 ft. 8 in.; breadth, 18 ft. 4 in.; height, 7 ft. 9 in. (5) A room is 21 ft. long, 15 ft. broad, and 10 ft. high; find the expense of painting the walls at 3d. a sq. ft.

(6) What would it cost at 4d. per sq. yd., to paint the walls of a room which is 13 ft. 6 in. long, 11 ft. 6 in. wide, and 9 ft. high?

(7) What would be the expense of painting, at 3s. a sq. yd., the walls of a room 27 ft. long, 17 ft. broad, and 113 ft. high, allowing for four windows, each 75 ft. by 4 ft.?

(8) A room is 36 ft. long, 18 ft. broad, and 12 ft. high. Find the whole cost of plastering the walls at 1s., and the ceiling at 1s. 6d. per sq. yd.

(9) Find the cost of painting the four walls of a room which is 32 ft. 4 in. long, 15 ft. 8 in. broad, and 11 ft. 6 in. high, at 3s. per sq. ft.

(10) How many sq. yds. of painting are there in a room 20 ft. long, 14 ft. 6 in. broad, and 10 ft. 3 in. high; allowing for a fireplace 4 ft. by 4 ft. 3 in., 2 windows each 6 ft. by 4 ft., and a doorway 6 ft. 6 in. by 4 ft.?

(11) Find the cost of papering a room 20 ft. long, 18 ft. broad, and 10 ft. high, at 4s. 6d. per sq. yd.

(12) Find the cost of papering a room 16 ft. long, 12 ft. broad, and 12 ft. high, at 9d. per sq. ft.

56. To find the length of paper required to cover the walls of a room.

RULE. Divide the total area of the wall-surface by the width of the paper, and the quotient will be the length required.

Ex. Find the expense of papering a room 20 ft. long, 15 ft. broad, and 12 ft. high, with paper 2 ft. wide at 6d. per yd.; allowing for 2 fireplaces, each 4 ft. 6 in. by 3 ft., 2 doors, each 7 ft. by 4 ft., and 4 windows, each 6 ft. 6 in. by 5 ft. Circuit of room = = 70 ft. Total area of wall-surface Area of fireplaces Area of doors Area of windows Total area to be

=70 ft. x 12 ft. =840 sq. ft. =4 ft. x 3 ft. x2=27 sq. ft. =7 ft. x 4 ft. x2=56 sq. ft. =63 ft. x 5 ft. ×4-130 sq. ft. deducted=27 sq. ft.+56 sq. ft.+130 sq. ft. =213 sq. ft.

Total area to be papered

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840 sq. ft.-213 sq. ft. -627 sq. ft.

=627÷2-313 ft.

=6d.÷3=2d.

= 2d × 3133 = 627d. =52s. 3d.
= £2 12s. 3d.

=

Ex. XXI.

(1) A room is 16 ft. long, 15 ft. broad, and 12 ft. high; how many yds. of paper 16 in. wide will be required to cover the walls?

(2) A room is 15 ft. long, 10 ft. broad, and 9 ft. 9 in. high; how many yds. of paper 26 in. wide will be required for it?

(3) What will it cost to paper a room 10 ft. high, and 84 ft. in circuit, at 9d. per sq. yd.?

(4) What length of paper 2 ft. wide will be required for a room 16 ft. square and 10 ft. 6 in. high, and what will it cost at 44d. per yd.?

(5) What is the cost of papering a room 15 ft. long, 12 ft. broad, and 10 ft. high with paper 30 in. wide at 74d per yd.?

(6) How much paper 21 in. wide will be required for a room 24 ft. long, 18 ft. wide, and 12 ft. high, allowing for a doorway 8 ft. by 4 ft., and three windows each 6 ft. by 3 ft.?

(7) What is the cost of papering a room 18 ft. long, 15 ft. wide, and 12 ft. high, with paper § yd. wide, at 73d. per yd.?

(8) Find the cost of papering a room 12 ft. 4 in high, 16 ft. long, and 14 ft. 3 in. broad, the paper being 2 ft. 6 in. wide, at 38. 9d. per yd., and the labour charged at 14d. per sq. ft.

(9) Find the expense of papering a room 41 ft. long, 17 ft. 4 in. broad, and 9 ft. high, with paper 20 in. wide, at 5d. a yard. (10) A room is 45 ft. long, 20 ft. 3 in. wide, and 11 ft. 3 in. high. Find the cost of papering the walls with paper wide, at 5d. a yard.

yd.

(11) A room is 20 ft. 6 in. long, 15 ft. 6 in. broad, and 16 ft. bigh; what will it cost to paper the room with paper half a yard wide, at 4d. a yd., allowing for two doors each 8 ft. by 3 ft. 9 in., and 3 windows, one 5 ft. by 7 ft., and the other two 5 ft. by 4 ft. each?

(12) Find the cost of papering a room 18 ft. long, 12 ft. wide, and 12 ft. high, with paper 18 in. wide, at 1d. per yd.

(13) A room 16 ft. square, requires for its walls six pieces of paper, 18 yds. 2 ft. long and 2 ft. broad; find the height of the room.

[Circuit of room 4 times the length of one side.

Area of wall surface = length of paper required x width of paper.
Height of room area of wall-surface + circuit of room.]

(14) The number of yds. of paper required to cover the four walls of a room 18 ft. long and 14 ft. broad, is 128, and the width of the paper is 16 in.; find the height of the room.

(15) The number of yds. of paper yd. wide required to cover the four walls of a square room 9 ft. high, is 96 yds. Find the length of each side of the room.

(16) If the cost of papering a room 10 ft. long, 8 ft. broad, and 8 ft. high, with paper at 6d. per yd. be 18s., find the width of the paper.

(17) If the expense of papering a room 18 ft. long, 14 ft. broad, and 8 ft. high with paper 16 in. wide be £6 8s., find the price of the paper per yd.

THE RHOMBUS AND RHOMBOID.

57. A Rhombus is a parallelogram which has all its sides equal, but its angles are not right angles.

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If a square picture-frame, ABCD, be taken and wrested out of the perpendicular, it will form the rhombus A B C D.

AB is called the base or length, and DP the perpendicular height.

58. A Rhomboid is a parallelogram which has its opposite sides only equal, and its angles are not right angles.

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If a rectangular picture-frame, EFGH, be taken and wrested out of the perpendicular, it will form the rhomboid E F G H.

EF is called the base or length, and HP the perpendicular height.

59. To find the area of a rhombus or rhomboid.

RULE. Multiply the base by the perpendicular height, and the pro

duct will be the

area.

For if the part ADE be cut from an oblique parallelogram ABCD, and A

D

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again placed so that AD may be on BC, it will form a rectangle, EFCD, thereby showing that the area of the oblique parallelogram ABCD is exactly equal to that of the rectangle EFCD. But the area of the rectangle EFCD, is found by multiplying DC by DE, and from the definition above, AB=DC. Hence the area of an oblique parallelogram is equal to the product of the base and the perpendicular height.

Ex. 1. Find the area of a rhombus whose base is 7 ft. 3 in. and perpendicular height 2 ft. 6 in.

7 ft. 3 in. 87 in.; 2 ft. 6 in. =30 in.

Area of rhombus 87 × 30=2610 sq. in. = 18 sq. ft. 18 sq. in.

Ex. 2. Required the area of a rhomboid whose length is 6 ch. 25 lks., and perpendicular height 2 ch. 50 lks.

6 ch. 25 lks.625 Iks. ; 2 ch. 50 lks.250 lks.

Area of rhomboid=625 × 250=156250 sq. lks.=1 ac. 2 ro. 10 po.

Ex. XXII.

(1) Find the area of a rhombus whose base is 12 ft. 6 in., and height 4 ft. 3 in.

(2) Required the acreage of a rhomb-shaped field whose side is 8 ch. 50 lks., and perpendicular breadth 5 ch. 25 lks. (3) What is the superficial content of a rhomboid whose side is 12.75 ft., and perpendicular breadth 9-5 ft.?

(4) Find the rental of a field in the shape of a rhomboid, whose base is 1375 links and perpendicular breadth 95 links, at £5 6s. 8d. per acre.

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