# Examples for 9th grade - page 85

1. Trapezoid - intersection of diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
2. Embankment Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long.
3. Candy Peter had a sachet of candy. He wanted to share with his friends. If he gave them 30 candies, he would have 62 candies. If he gave them 40 candies, he would miss 8 candies. How many friends did Peter have?
4. How far From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
5. Rhombus construction Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides...
6. Competitors In the first round of slalom fell 15% of all competitors and in the second round another 10 racers. Together, 40% of all competitors fell. What was the total number of competitors?
7. 6 terms Find the first six terms of the sequence. a1 = 7, an = an-1 + 6
8. Modulo Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 .
9. Photocopier A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page?
10. Fence and scale The garden with 80 m of fencing is draw on plan as a square with a side length of 4 cm. At what scale is this plan made?
11. Rhombus The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
12. Diamond diagonals Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
13. Soaps Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the sma
14. Lighthouse The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lightho
15. Hypotenuse - RT A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
16. A bridge A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H
17. Paul earned Paul earned 300 Kč in one hour, Václav 1/3 more than Paul. Václav worked 60 hours, which is 1/3 fewer hours than Paul worked. How many percents less earned Paul an hour than Václav? How many hours did Paul more than Václav? How much did Paul earn more t
18. Children The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group? The angle of a straight road is approximately 12 degrees. Determine the percentage of this road. The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?