Geometry: Chapter 11 Study Guide
Rectangles, Squares, and Triangles
1. Find the area of a rectangle with base in and height in.3. Find the area of a triangle with base 18in and height 3in.
5. Find the area of a rectangle with diagonal 26m and side 10m.
7. Find the area of an isosceles triangle with base 12cm and perimeter 32cm. / 2. Find the area of a square with sidecm.
4. Find the area of an equilateral triangle with perimeter 24ft.
6. Find the area of a square with diagonal 8ft.
8. Find the area of an isosceles right triangle with hypotenuse 10ft.
9. Find the area of the enclosed region: (all corners are right angles)
/ 10. Find the area of the shaded region: (all corners are right angles)
11. A path 3m wide surrounds a rectangular garden 15m wide and 18m long. What is the area of the path? / 12. The length of a rectangle is 3m more than its width. If its area is 54m2, find the dimensions of the rectangle.
Parallelograms and Rhombuses
13. Find the area of a parallelogram with base 14. Find the area of a rhombus with diagonals of
and height . 6m and 4.5m.
15. Find the area of a parallelogram with sides 16. Find the area of a rhombus with perimeter of
12m and 8m with an angle of 45 degrees. 80 and one diagonal of length 32ft.
17. Find the area of a rhombus with perimeter 36m and one angle of 120 degrees. / 18. Find the area of the region. (It is a parallelogram topped with a triangle.):
Trapezoids
21. Find the area of an isosceles trapezoid with bases 9 and 19 and legs of 13cm. / 22. Find the area of an isosceles trapezoid with the shorter base of , height of 6, and base angles of 60◦
Regular Polygons
23. Find the area of an equilateral triangle with apothem 4m. / 24. Find the area of a square with radius 8m.25. Find the area of regular hexagon with perimeter 48ft. / 26. Find the area of a regular hexagon with apothem 9cm.
Circles, Arcs, and Sectors (Leave answers in terms of )
27. Find the diameter, circumference, and area of a circle with radius 7cm. / 28. Find the radius, diameter, and circumference of a circle with area 24ft2.29. In a circle with diameter 10m, a central angle is 60◦. Find the length of the resulting minor arc and the area of this sector. / 30. Find the area of the shaded region:
31. Find the area of the shaded region: / 32. Find the area of the shaded region:
Scale Factor, Ratio of Perimeters and Areas
33. The scale factor of two similar polygons is 2:7. What is the ratio of:a) their corresponding sides?
b) their perimeters?
c) their areas? / 34. The scale factor of two similar polygons is 3:5. The area of the larger polygon is 75m2. Find the area of the smaller polygon.
35. The areas of two regular hexagons are 9cm2
and 25cm2. What is the ratio of:
a) their sides?
b) their perimeters? / 36. The perimeters of two similar parallelograms are 4m and 8m. What is the:
a) scale factor?
b) ratio of their areas?