How would you find the relationship between the areas of two similar geometric figures? Consider the following two similar rectangles.
The area of the smaller rectangle is. The area of the larger rectangle is
How could you have predicted this result? Look at the ratio of small width to large width:.
The small rectangle has sides that are
the small rectangle to the area of the large rectangle is
Thus we can develop the following principle:
The areas of two similar figures are in the same ratio as the square of the ratio of two
corresponding sides. Use this information to complete exercises 29 and 30.
Each pair of geometric figures is similar. Find the unknown area. Round to the nearest
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
Prealgebra (6th Edition)
- Mary Frances has a rectangular garden plot that encloses an area of 48 yd2. If 28 yd of fencing are purchased to enclose the garden, what are the dimensions of the rectangular plot?arrow_forwardThe ratio of the circumferences of two circles is 2:1. What is ratio of their areas?arrow_forwardThe cross section of a dovetail slide is shown. Before the dovetail was cut, the cross section was rectangular in shape. Find the cross-sectional area of the dovetail slide. Round the answer to 1 decimal place.arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALIntermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill