### Mathematics Teacher

#### Geometry Bibliography: Area

Hubert Ludwig, Ball State University

 ```Connecting Geometry and Algebra: Geometric Interpretations of Distance Terry W. Crites Primarily as areas under curves. (88, 1995) 292 - 297 Using Similarity to Find Length and Area James T. Sandefur Similar figures and scaling factors. Constructing spirals in triangles and squares. Involvement with the theorem of Pythagoras. (87, 1994) 319 - 325 Spiral Through Recursion Jeffrey M. Choppin Finding areas and perimeters of spirals created through recursive processes. (87, 1994) 504 - 508 Teaching Relationships between Area and Perimeter with The Geometer's Sketchpad Michael E. Stone For all n-gons with the same perimeter, what shape will have the greatest area? Sketchpad investigations of the problem. (87, 1994) 590 - 594 Multiple Solutions Involving Geoboard Problems Lyle R. Smith Finding areas and perimeters of polygons formed on a geoboard. (86, 1992) 25 - 29 Area and Perimeter Connections Jane B. Kennedy Activities for investigating maximum area rectangles with fixed perimeter. (86, 1993) 218 - 221, 231 - 232 The Use of Dot Paper in Geometry Lessons Ernest Woodward and Thomas Ray Hamel Area, perimeter, congruence, similarity, Cevians. (86, 1993) 558 - 561 Looking at Sum k and Sum k*k Geometrically Eric Hegblom Using squares and determining area, using cubes and determining volume. (86, 1993) 584 - 587 The Generality of a Simple Area Formula Daniel J. Reinford Sharing Teaching Ideas. Using the triangle area formula K = rs to find the areas of polygons which have inscribed circles and applying the formula to find the area of a circle. (86, 1993) 738 - 740 A Circle is a Rose Margaret M. Urban Area conjectures for a rose curve. (85, 1992) 114 - 115 Making Connections: Beyond the Surface Dan Brutlag and Carole Maples Dealing with scaling-surface area-volume relationships. (85, 1992) 230 - 235 Determining Area and Calculating Cost: A "Model" Approach Harry McLaughlin Activities for discovering the formula for the area of a rectangle and using the information to calculate various costs. (85, 1992) 360 - 361, 367 - 370 A Generalized Area Formula Virginia E. Usnick, Patricia M. Lamphere, and George W. Bright Looking for a common structure in familiar area formulas. (85, 1992) 752 - 754 Area and Perimeter Are Independent Edwin L. Clopton Sharing Teaching Ideas. A demonstration and laboratory activity. (84, 1991) 33 - 35 A Geometric Look at Greatest Common Divisor Melfried Olson Activities involving area. (84, 1991) 202 - 208 A Fractal Excursion Dane R. Camp Area and perimeter results for the Koch curve and surface area and volume results for three-dimensional analogs. (84, 1991) 265 - 275 Pick's Theorem Extended and Generalized Christopher Polis The extension is to lattices other than square lattices. The author was an eighth-grade student at the time the article was written. (84, 1991) 399 - 401 Counting Squares David L. Pagni Finding a relationship between the size of a rectangle and the number of subsquares cut by a diagonal. (84, 1991) 754 - 758 Area of a Triangle Donald W. Stover Sharing Teaching Ideas. An alternate method for finding the area of a triangle given the lengths of the sides. (83, 1990) 120 Seven Ways to Find the Area of a Trapezoid Lucille Lohmeier Peterson and Mark E. Saul Sharing Teaching Ideas. Furnishing a hands-on experience in determining the area of a trapezoid. (83, 1990) 283 - 286 Areas and Perimeters of Geoboard Polygons Lyle R. Smith Finding polygons with specific areas and specific perimeters on a geoboard. (83, 1990) 392 - 398 Some Discoveries with Right-Rectangular Prisms Robert E. Reys Activities for problem-solving experiences with area and volume. (82, 1989) 118 - 123 What Do We Mean by Area and Perimeter? Virginia C. Stimpson Sharing Teaching Ideas. A lesson designed to reveal misconceptions about the relationship between area and perimeter. (82, 1989) 342 - 344 Area Formulas on Isometric Dot Paper Bonnie H. Litwiller and David R. Duncan Isometric graph paper as a teaching aid for the concept of area. (82, 1989) 366 - 369 Interpreting Proportional Relationships Kathleen A. Cramer, Thomas R Post, and Merlyn J. Behr Activities which include some discussion of surface area and map scaling. (82, 1989) 445 - 452 Designing Dreams In Mathematics Linda S. Powell Sharing Teaching Ideas. Informal geometry project involving area calculations. (82, 1989) 620 Geometrical Adventures in Functionland Rina Hershkowitz, Abraham Arcavi, and Theodore Eisenberg Determining the change in area produced by making a change in some property of a particular figure. 80, (1987) 346 - 352. Approximation of Area Under a Curve: A Conceptual Approach Tommy Dreyfus Various approaches are presented. 80, (1987) 538 - 543. Using Sweeps to Find Areas Donald B. Schultz A technique related to a theorem of Pappus. 78, (1985) 349 - 351. Investigating Shapes, Formulas, and Properties With LOGO Daniel S. Yates Logo activities leading to results on areas and triangle geometry. 78, (1985) 355 - 360. (See correction p. 472.) Measuring the Areas of Golf Greens and Other Irregular Regions W. Gary Martin and Joao Ponto Divide the region into triangles having a common vertex at an interior point of the region. BASIC program provided. 78, (1985) 385 - 389. Ring-Around-A-Trapezoid Vincent J. Hawkins Finding the area of a circular ring by transforming it into an isosceles trapezoid. 77, (1984) 450 - 451. How Is Area Related to Perimeter? Betty Clayton Lyon Relations involving rectangles with integral sides. 76, (1984) 360 - 363. Understanding Area and Area Formulas Michael Battista A sequence of lessons to discourage some common misunderstandings about area. 75, (1982) 362 - 368, 387. Area = Perimeter Lee Markowitz When will the area of a triangle be equal to its perimeter? 74, (1981) 222 - 223. The Second National Assessment In Mathematics: Area and Volume James J. Hirstein A discussion of student results on the concepts. 74, (1981) 704 - 708. The Isoperimetric Theorem Ann E. Watkins Activities to aid in the discovery that for a given perimeter the circle encloses the greatest area. 72, (1979) 118 - 122. A Different Look At pi r*r William D. Jamski Dividing a circle into n congruent segments, then reassembling them into a "quadrilateral". 71, (1978) 273 - 274. Finding Areas Under Curves With Hand-Held Calculators Arthur A. Hiatt Develops (in the appendix) a method for finding the area of a polygon, given the coordinates of its vertices. 71, (1978) 420 - 423. Problem Posing and Problem Solving: An Illustration Of Their Interdependence Marion I. Walter and Stephen I. Brown Given two equilateral triangles, find a third whose area is the sum of the areas of the first two. The Pythagorean theorem and a generalization. 70, (1977) 4 - 13. Tangram Mathematics Activities involving area relationships. 70, (1977) 143 - 146. The Surveyor and The Geoboard Ronald R. Steffani Surveyors method for finding area related to the geoboard. 70, (1977) 147 - 149. Sum Squares On A Geoboard James J. Cemella The number of squares on a geoboard and their area. 70, (1977) 150 - 153. Tangram Geometry James J. Roberge Using the tangram pieces to create geometric figures. Looks at convex quadrilaterals in particular. 70, (1977) 239 - 242. Volume and Surface Area Gerald Kulm Activities involving surface areas and volumes of rectangular boxes with open tops. 68, (1975) 583 - 586. Pick's Rule Christian R. Hirsch Activities for discovering and using Pick's rule. 67, (1974) 431 - 434, 473. Area Ratios In Convex Polygons Gerald Kulm Area ratios involved when one regular n-gon is derived from another by joining division points of sides. 67, (1974) 466 - 467. Problem Number 10 George Lenchner Find the area of a quadrilateral derived from a right triangle. 67, (1974) 608 - 609. Some Suggestions For An Informal Discovery Unit On Plane Convex Sets Alton T. Olson Activities leading to the discovery of properties and existence of convex sets. 66, (1973) 267 - 269. That Area Problem Benjamin Greenberg Finding the area of a quadrilateral formed by trisecting the sides of a given quadrilateral. 64, (1971) 79 - 80. Area From A Triangular Point Of View Margaret A. Farrell Using an equilateral triangle as the unit of area. 63, (1970) 18 - 21. Two Incorrect Solutions Explored Correctly Merle C. Allen Converse of Pythagoras, area of a triangle. 63, (1970) 257 - 258. The Area Of A Pythagorean Triangle and The Number Six Robert W. Prielipp The area of such a triangle is a multiple of six. 62, (1969) 547 - 548. A Medieval Proof Of Heron's Formula Yusuf Id and E.S. Kennedy A proof by Al-Shanni. 62, (1969) 585 - 587. Pierced Polygons Charles G. Moore Regions formed when a polygonal region is cut from the interior of another polygonal region. Angle relations. 61, (1968) 31 - 35. The Area Of A Rectangle Lawrence A. Ringenberg Formula developed using the square as a unit. 56, (1963) 329 - 332. The Trapezoid and Area Wilfred H. Hinkel An approach to polygonal area formulas. 53, (1960) 106 - 108. Area Device For A Trapezoid Emil J. Berger Teaching aid. 49, (1956) 391. H.J.L. 07/15/97 email: 00hjludwig@bsu.edu home page: http://www.cs.bsu.edu/~hjludwig/ ```