Wentworth's Plane and Solid Geometry · Book IV, Exs. 424–437 · Book 5: Book IV: Areas of Polygons
66. Problems of computation: areas (2)
Goal: Your student solves numerical problems on areas of similar figures, trapezoids and rhombuses.
You'll need
- The book, open to these pages
- Pencil and paper
- A calculator (optional)
What's in the book
Page 210: numerical exercises 424–437. This finishes Book IV.
The lesson, step by step
Warm up
Ask: Two similar figures have sides in the ratio 3 : 5. What is the ratio of their areas?
Similar figures
Ex. 428. In two similar polygons, two homologous sides are 15 feet and 25 feet. The area of the first polygon is 450 square feet. Find the area of the second polygon.
A real floor
Ex. 435. Find the number of square feet of carpet that are required to cover a triangular floor whose sides are, respectively, 26 feet, 35 feet, and 51 feet.
More
Your student does four or five of Ex. 424–437.
Review Book IV
Ask for the area formulas of the rectangle, parallelogram, triangle and trapezoid, and the reason similar figures are as the squares of their sides.
Wrap up
Check the answers together.
Answers to the book's problems
Ex. 424: 240/13, about 18.46 ft. Ex. 425: 20 ft. Ex. 426: AP = AB/√2, about 0.707 AB. Ex. 427: one fourth. Ex. 428: 1250 sq ft. Ex. 429: 20 sq ft. Ex. 430: 5 ft. Ex. 431: 3 : 4 (the triangle whose side equals the other's altitude is the smaller). Ex. 432: 31 1/9 and 52 8/9 sq ft. Ex. 434: area 5400 sq yd; side 75 yd; distance 72 yd. Ex. 435: 420 sq ft. Ex. 436: am/(h + m). Ex. 437: ½(p + q)√(pq).
Worked out for this site from the scan. If a number in your copy differs, trust the book.