Handouts
LINK: Plane and Solid Geometry
Topics:
Triangle
Rectangle
Square
Quadrilaterals
Regular Polygons
Circle
Ellipse
Polyhedron
Exercises
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1. Find the area of a pentagon having a perimeter of 60-in. a. 234.8 in2 b. 247.7 in2 c. 220.2 in2 d. 212.7 in2 2. If the numbers of diagonals in a polygon is 9, what is the description of the polygon? a. Hexagon b. Nonagon c. Pentagon d. Decagon 3. The area of a circle is 160 in2, what is the length of a side of regular hexagon inscribed in this circle? a. 5 in b. 6 in c. 8 in d. 7 in 4. What is the largest diameter of a circle that will fit inside a regular pentagon with 5-in sides. a. 6.9 in b. 5.3 in c. 7.8 in d. 8.1 in 5. How many diagonals are there in a polygon of 18 sides? a. 130 b. 125 c. 135 d. 140 6. A heptagon is circumscribed in a circle whose area is 160 cm2. Determine the length of side of heptagon. a. 5.3 cm b. 7.2 cm c. 6.9 cm d. 8.3 cm 7. A hexagon has an apothem of 6-in. Find the length of side of the polygon. a. 8.3 in b. 5.3 in c. 6.9 in d. 7.2 in 8. The sum of interior angle of nonagon is _____. a. 1360 deg b. 1260 deg c. 1420 deg d. 1800 deg 9. Find the interior angle of a decagon _____. a. 360 deg b. 180 deg c. 165 deg d. 144 deg 10. What is the radius of a circle inscribed in a triangle with sides of 7, 10 and 14-in? a. 2 in b. 3 in c. 4 in d. 5 in 11. A trapezoid has a bottom base of 12-in and top base of 7-in. If the height is 6-in, find the area. a. 57 in2 b. 60 in2 c. 55 in2 d. 52 in2 12. Find the length of side of an equilateral triangle whose area is equal to 420-in2. a. 28.2 in b. 34.1 in c. 38.9 in d. 31.1 in 13. A rectangle has a width of 12 m and area of 100 m2. If the perimeter of rectangle is equal to the perimeter of equilateral triangle, find the area of equilateral triangle. a. 65.2 m2 b. 79.6 m2 c. 74.3 m2 d. 67.3 m2 14. The area of a circle is 310-in2. What is the circumference? a. 58.2 in b. 73.1 in c. 62.4 in d. 68.9 in 15. The area of a circle is 260-in2. What is the diameter of the circle? a. 16.3 in b. 18.2 in c. 20.6 in d. 14.3 in 16. What is the area of an ellipse with an aspect ratio of 2.5 and total perimeter of 28-inches? a. 50.8 in2 b. 45.3 in2 c. 48.2 in2 d. 43.0 in2 17. A rhombus has diagonals of 34 and 25-inches. Find the area. a. 425 in2 b. 428 in2 c. 433 in2 d. 430 in2 18. The area of a triangle inscribed in a circle is 40 cm2 and the radius of the circumscribed circle is 8.15 cm. If the two sides of the inscribed triangle are 9 cm and 12 cm, respectively, calculate the third side. a. 10 cm b. 12 cm c. 14 cm d. 16 cm 19. The sides of a triangle are 10 cm, 12 cm and 16 cm. Find the radius of the inscribed circle. a. 2.18 cm b. 3.15 cm c. 4.00 cm d. 5.23 cm 20. A square has a diagonal of 18 inches. Find the length of its sides. a. 10.8 in b. 11.5 in c. 13.4 in d. 12.7 in 21. A rectangular lot has a width of 16 m and length of 25 m. Find the diameter of a circular lot whose area is twice that of rectangular lot. a. 28.1 m b. 34.3 m c. 25.3 m d. 31.9 m 22. Find the area of equilateral triangle whose sides is 12-in. a. 62.4 in2 b. 64.3 in2 c. 66.2 in2 d. 68.5 in2 23. In triangle ABD, A=35o, B=82o and b=12-in. Find the area of the triangle. a. 28.3 in2 b. 25.8 in2 c. 34.3 in2 d. 38.8 in2 24. Find the area of triangle whose sides are 32 cm, 37 cm and 48 cm. a. 560.3 cm2 b. 591.6 cm2 c. 538.2 cm2 d. 521.8 cm2 25. Find the area of circle inscribed in a square whose area is 250-in2. a. 190.3 in2 b. 200.0 in2 c. 196.3 in2 d. 193.8 in2 26. A large 25 m diameter cylindrical tank that sits on the ground is to be painted. If one liter of paint covers 12 m2, how many liters are required if it is 12 m high (include the top). a. 119.5 L b. 123.5 L c. 128.5 L d. 130.5 L 27. A square has a perimeter of 60-in. If the area of square is equal to the circle, determine the circumference of the circle. a. 50 in b. 58 in c. 55 in d. 53 in 28. A closed cylinder has a height of 4 m and diameter of 8 m. Find the inner surface area. a. 180 m2 b. 192 m2 c. 198 m2 d. 200 m2 29. A pyramid has a rectangular base of 12 in x 14 in. If the height is 16-in, find the volume of pyramid. a. 800 in3 b. 880 in3 c. 885 in3 d. 896 in3 30. A spherical water tank 12 m diameter is filled to a height of 3/2 of its radius. Find the volume of water in the tank. a. 750 m3 b. 765 m3 c. 785 m3 d. 763 m3 31. A steel plate made of 1.5-in x 5 ft x 12 ft has a density of 0.285 lb/in3. Find the weight of the material. a. 3693.6 lbs b. 3505.2 lbs c. 3400.1 lbs d. 3720.8 lbs 32. A cylindrical truncated prism has a base diameter of 12 m. The shortest height is 6 m and the longest height is 12 m, find the volume of the prism. a. 1038.2 m3 b. 1128.9 m3 c. 1017.9 m3 d. 1213.7 m3 33. A cube has a diagonal of 6 ft, determine the diameter of a sphere whose volume is thrice that of the cube. a. 6.20 ft b. 3.01 ft c. 8.32 ft d. 4.30 ft 34. A sphere whose diameter increases from 5 cm to 7 cm? What is the percent increase in the surface area. a. 90% b. 96% c. 93% d. 98% 35. What is the total surface are including the base, of a 7 foot high right circular cone with a 5 feet base? a. 75.3 ft2 b. 82.1 ft2 c. 78.5 ft2 d. 80.1 ft2 |
