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Altitude/

A Polygon is a plane surface bounded by three or more straight lines.

The Perimeter of a polygon is the distance around it. A polygon of three sides is called a Triangle.

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The Base of a triangle is the side upon which it seems

to stand, as AB (Fig. 1).

The Vertex is the point opposite the base, as F (Fig. 2). The Altitude is the perpendicular distance from the vertex to the base, as FM (Fig. 2).

LESSON 107

Considered with reference to the relative size of their angles, triangles are distinguished as right-angled, acuteangled, or obtuse-angled.

A Right-angled Triangle, or right triangle, has one right angle (Fig. 1).

An Acute-angled Triangle has three acute angles (Fig. 2). An Obtuse-angled Triangle has one obtuse angle (Fig. 4). Considered with reference to the relative length of their sides, triangles are distinguished as equilateral, isosceles, or scalene.

An Equilateral Triangle has three equal sides (Fig. 2).
An Isosceles Triangle has two equal sides (Fig. 3).
A Scalene Triangle has three unequal sides (Fig. 4).

A polygon of four sides is called a Quadrilateral.

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The first four of the figures above are called Parallelograms, because their opposite sides are parallel.

The Base of a parallelogram is the side upon which it seems to stand, as ab, Fig. A.

The Altitude of a parallelogram is the perpendicular distance between the base and the side opposite, as de, Fig. C.

The Diagonal of a quadrilateral is a straight line joining its opposite angles, as ac, Fig. A, and fg, Fig. D.

LESSON 108

A Rectangle is a plane surface having four right angles, as Fig. A, above.

A Square is a rectangle whose four sides are of equal length, as Fig. B, above.

A Rhomboid is an oblique-angled parallelogram, as Fig. C.

A Rhombus is a rhomboid whose four sides are of equal length, as Fig. D.

A Trapezoid is a quadrilateral having only two of its sides parallel, as Fig. E, p. 121.

A Trapezium is a quadrilateral having none of its sides parallel, as Fig. F, p. 121.

1. Why are the pages of this book quadrilaterals ? Why parallelograms ?

2. Point out any parallelograms in your schoolroom, and tell why they are parallelograms.

3. In what particular respect are a rectangle and a square alike? Wherein are they unlike?

4. If you cut a rectangle of paper through the diagonal into two parts, what plane figure is each part, and what part of the rectangle is each part?

5. Compare the base of each triangle with the length of the rectangle.

6. Compare the rectangle with the rhomboid, and state wherein they are unlike.

7. If you cut a square into two equal triangles, what kind of triangle is each?

8. In what respect are a trapezoid and a rhomboid unlike ?

9. Wherein does a rhombus resemble a square?

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3. What is a two-mile square? What are two square miles?

4. In what particular respect are a square yard, a square rod, and a square mile alike? In what respect are they different?

The area of a polygon is the number of square units of surface of a certain value it contains. The square inch, the square foot, the square yard, the square rod, the square chain, the acre, and the square mile are the principal English surface measure units used in computing areas. Area of a Rectangle. The area of a rectangle is the prod uct of its base and altitude.

1. Draw a rectangle 6 in. long and 3 in. wide. Divide the edges into parts 1 in. long, and draw lines connecting the opposite points of division, as shown in the diagram.

D

A

6 in.

3 in.

B

2. What is the shape of the parts into which you have divided the rectangle?

3. How many of these parts have you? Count them, writing inside of each square its number from one upwards.

4. How many rows have you with six in each row? 5. How many rows have you with three in each row? 6. What is the area of your rectangle?

7. Can you make a rule for finding the area of a rectangle?

8. Will your rule apply to a square as well?

LESSON 110

1. What is the area of a field 48 rd. long and 36 rd. wide?

2. What is the value of a square field 80 rd. long, at $37 an acre?

3. A piece of land is 70 yd. long and 60 yd. wide, and has the shape of a rectangle. Draw a plan of the field on the scale of 20 yd. to the inch, that is, let 1 inch represent 20 yd. on your plan. What is the area of your plan? What is the area of the field?

4. Given the area and one side of a rectangle, how do you find the other side?

5. What is the length of a field whose width is 60 rd. and whose area is 5400 sq. rd?

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As the area of a rectangle is equal to the product of its base and altitude, this is also the area of the rhomboid.

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