Calculate the Perimeter and Area of Each of the Following
Geometry: Chapter 9 Review
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Leave all answers in π unless otherwise specified.
1. Find the area.2. Find the area.
3. Find the area.
4. Find the area of the shaded section.
5. A trapezoid is cut from a 10 – inch by 2 – inch rectangle. The length of one base is 10 inches. What is the area of the trapezoid? Round to the nearest hundredth.
/ 6. For a party, Samantha wants to have finger sandwiches. She cuts sandwiches into 5 – inch circles. If she cuts each circle into 3 congruent pieces, what is the area of each piece? Round to the nearest hundredth.
7. Martha is making a roof for her clubhouse that is made up of 4 congruent equilateral triangles. The perimeter of one triangle is 18 feet. Find the area of one side of the roof and round to the nearest hundredth. / 8. Sampson’s dog, Cecil is tied to the corner of his 7 meter by 7 meter square house by a chain 7 meters long. How much play area does Cecil have? Round to the nearest hundredth.
9. A landscape architect is designing three trapezoidal flowerbeds to wrap around three sides of a hexagonal flagstone patio, as shown. If the architect’s fee is $100 plus $5 per square foot. What will the flowerbeds cost?
/ 10. In a rectangular farm land that is 10 x 28 kilometers long, 2 km. crop circles have been drawn. How much of the farm land is not part of a crop circle? Round to the nearest hundredth.
11. A satellite orbiting earth uses radar to communicate with 2 control stations on Earth’s surface. The satellite is in a geostationary orbit. From the perspective of Station 1, the satellite is on the horizon and from Station 2, it is directly overhead. The distance from Station 2 to the satellite is 15, 300 mi., and assume the Earth’s radius is 3959 miles.
a. A technician is flying from one station to the other along a direct path along the Earth’s surface. How far does the technician fly from station 1 to station 2? Round to the nearest hundredth.
b. How long does it take the technician to fly if he averages a speed of 54 mph? Round to the nearest hundredth.
c. How far does a signal travel if it leaves Station 1, goes to the satellite and then goes to station 2? Round to the nearest hundredth.
12. At a greyhound race track, 2 gates are set up along the circular track. The Gate 1 holds all the greyhounds and the Gate 2 holds the lure or the hare that the dogs chase. These gates are connected by wires to the control tower that sends signals to release the gates. Use the given figure below and the fact that the diameter of the track is 70 meters to answer the following questions.
a. How far are must the dogs run before they reach the lure’s gate?
b. How long does it take the dogs to reach the gate if their speed is 45 mph?
c. How long is the wire that connects Gate 1 to the tower to Gate 2?
13. In a patch of forest that measures 47 by 58 meters, there are a total of 1450 jackrabbits. Find the population density. / 14. In a 700 square mile cornfield, there is a population density of 47 weeds per square mile. How many weeds are there?15. Find the population density of China if there are 1,321,851,888 people living in a 5,796,162 square mile area. / 16. New Zealand has a total population of 4,283,360. If the population density is 16 people per square kilometer, how large is New Zealand?
17. A farmer owns a rectangular field that measures 12.5 x 25 miles and has grapefruit, orange and lemon trees. The farmer has 10 rows of grapefruit trees with 32 in each row, 15 rows of orange trees with 40 in each row and 35 rows of lemon trees with 28 in each row. What is the overall density of the field?