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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 & room 16 ft. square and 10 ft. 6 in. high, and what will it cost at 41d. 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 7}d 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 43 ft., and three windows each 6 ft. by 33 ft. ?

(7) What is the cost of papering a room 18 ft. long, 15 ft. wide, and 12 ft. high, with paper 5 yd. wide, at 7 d. 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 3s. 9d. per yd., and the labour charged at itd. 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 ; yd. wide, at 5d. a yard.

(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 14d. 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 papor. 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 188., 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.

Square

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

A B is called the base or length, and D P the perpendicular height.

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

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Rectangle

Rhomboid If a rectangular picture-frame, EFGH, be taken and wrested out of tho 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 product will be the area.

For if the part ADE be cut from an oblique parallel. ogram A B C D, and A E

F again placed so that A D may be on BC, it will form a rectangle, EFCD, thereby showing that the area of the oblique parallelogram A B C D is exactly equal to that of the rectangle EFCD. But the area of the rectangle EFOD, is found by multi. plying D O by D E, 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.

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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 Iks.

(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 68. 8d. per acre.

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