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LESSON 111

1. What is the area of a rhomboid whose length is 72 rd. and width 48 rd.?

2. A piece of land is 800 rd. long and 60 rd. wide, and has the shape of a rhomboid. What is its value at $50 an acre?

3. A room 15 ft. long requires 20 sq. yd. of carpet to cover the floor. How wide is the room?

4. What is the area of a rhomboid whose length is 9 chains and width 5 chains? Express the area: 1st, in square chains; 2d, in square feet; 3d, in square rods; 4th, in acres.

5. The area of a room 36 ft. long is 120 sq. yd. What is the width of the room?

Area of a Rhombus. As a rhombus is a rhomboid whose four sides are of equal length, the area of a rhombus is equal to the product of the base and altitude.

ltitude

Rhombus

Base

6. How many square rods are there in a field in the form of a rhombus, each side measuring 64 rods, and the perpendicular between opposite sides 50 rods? How many acres?

7. The base of a rhombus is 30 yd. and altitude 70 ft. Find its area.

8. The base of a rhomboid is 30 ch. and the altitude 25 rods. What is its area?

9. What is the area of the walls of a room 30 ft. long, 241 ft. wide, and 14 ft. high? What is the area of the ceiling?

10. Find the cost of plastering the walls and ceiling of the room described in Ex. 9, at 20 a square yard.

LESSON 112

Area of a Triangle. The area of a triangle is equal to one half of the product of its

base and altitude.

The Base is any one of its sides.

The Altitude is the perpendicular distance from the base to

A

B

D

the vertex of the opposite angle. Thus, in the triangle ABC, the base is AB, and the altitude CD.

1. Draw on paper a parallelogram ABCD of any convenient size as shown in the diagram.

Taking AB for the base, draw the altitude DE, and the diagonal DB. Cut out the parallelogram from the paper, and cut it into two parts along the diagonal DB. Now turn one part around and place it directly on top of the other, and you will see that the two triangles are equal. There are several kinds of triangles; but all can be formed by cutting quadrilaterals into two parts from corner to corner.

D

B

E

C

As the area of a parallelogram is equal to the product of its base and altitude, so the area of a triangle, which is one half the parallelogram, is one half the product of the base and altitude of the parallelogram, that is, one half the product of its own base and altitude.

2. What is the area of a triangle whose base is 24 ft. and altitude 14 ft.?

3. The base of a triangle is 20 rd. and the altitude is 12 rd. What is the area of the triangle?

4. Find the area of a triangle whose base is 24 yd. and altitude 2 rd.

5. How many acres are there in a triangular piece of land having a base of 80 rd. and an altitude of 56 rd.?

LESSON 113

Draw the following triangles on a scale of in. to the foot, and calculate their areas. Write the area and the value of the given parts in and about the diagrams:

Altitude 3 ft.

Area 9 sq.ft.

Base 6 ft.

Scale in. to foot

MODEL

1. Base 6 ft. and altitude 3 ft. 2. Base 4 ft. and altitude 2 ft. 3. Base 8 ft. and altitude 4 ft.

4. Base 5 ft. and altitude 3 ft.

5. A right triangle, the sides of the right angle being 5 ft. and 4 ft.

6. A right isosceles triangle whose equal sides are 5 feet. Area of a Trapezoid. The area of a trapezoid is equal to its altitude multiplied by one half of the sum of the parallel sides.

[blocks in formation]

7. Draw on paper a trapezoid ABCD of any convenient size, in which AB and CD are the parallel sides.

[blocks in formation]

trapezoid from the paper, and cut off the triangle HBF,

E

D

H

and place it in the position H' CF. You have now changed the trapezoid into a parallelogram. The two parallel sides of the trapezoid have been made the equal sides of the parallelogram, and one half the sum of the parallel sides is equal to AH, which is the base of the parallelogram. The altitude DG remains unchanged.

G

H

As the area of a parallelogram is the product of its altitude and base, so the area of a trapezoid is the product of its altitude and one half the sum of its bases.

LESSON 114

1. Find the area of a trapezoid whose parallel sides are 70 ft. and 150 ft., and altitude 40 ft.

2. I have a flower bed in the shape of a trapezoid. The two parallel sides are 12 ft. and 14 ft., and the perpendicular distance between the parallel sides is 10 ft. Find the area.

3. The sum of the parallel sides of a trapezoid is 150 yards, and the perpendicular 75 yards. How many square yards are there in the area?

4. One parallel side of a field in the shape of a trapezoid is 150 rd., the other 200 rd. How many square rods are there in the field, the perpendicular distance between the sides being 50 rd.? How many acres?

Make a diagram on a scale of 50 rd. to an inch.

5. Find the cost of cementing a cellar bottom 54 ft. long and 181 ft. wide, at 621 a square yard.

Since the area of a parallelogram is equal to the product of its length and breadth, either side will equal the area divided by the other side.

6. A blackboard has a surface of 105 sq. ft. What is the width of the board if it is 30 ft. long?

7. What is the length of a trapezoid whose parallel sides are respectively 24 ft. and 32 ft.?

8. How many feet are there in the perimeter of an equilateral triangle, each side of which is 5 yards long? 9. How many strips of carpet, yd. wide, will be needed for a room 18 ft. wide?

10. If the above room is 22 ft. long, how many yards of carpet will be needed to cover the floor?

LESSON 115

1. If the base of a triangle is 12 yards and the altitude 8 yards, what is the area of the triangle?

GRAD. ARITH. V. - -9

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