GRADE 8 GEOMETRIC SENSE (1998)
Make sure you include proper units in your answer!
1. Refer to the figure and the information below to determine the angle measures asked for in (a) and (b) below.
Triangle ABG is an isosceles triangle.|
Triangle ADE is a right triangle.
Angle BAC = 51°
Angle BGA = 72°
(a) Angle 1 = ________________
(b) Angle 2 = ________________
2. A group of students on a hiking trip wants to find the distance BA across a pond. (See the figure). One student marks a point C 120 m away from point A and connects point C with point B. She then finds point D so that angle BCD angle BCA and the distance DC = 120 m (the distance of ). If has length 180 m and has length 220 m, what is the distance BA across the pond?
3. A rectangular box has six surfaces. The area of its front is 54 square inches; the area of its side is 72 square inches; and the area of its top is 108 square inches. What is the volume of the box?
4. The Babylonians and ancient Hebrews calculated the circumference of a circle by figuring the perimeter of a regular hexagon with all six vertices on the circle. The regular hexagon shown has a perimeter which is almost the circumference of the circle. If the radius of the circle is 10 inches, what percent of the circumference of the circle is the difference between the perimeter of the hexagon and the circumference of the circle? (Give your answer to the nearest 1/10 of a percent.)
5. If the hexagon ABCDEF (in the previous problem) were rotated around point D, what angle and what direction would be needed to rotate point C onto point E? (Note: Give direction as clockwise or counterclockwise.)