# Examples for 9th grade - page 42

- Rhombus

ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus. - Midpoint of segment

Point A has coordinates [-16; 23] and the midpoint of the segment AB is the point [2; 12]. What are the coordinates of point B? - Semicircle

To a semicircle with diameter 10 cm inscribe square. What is the length of square sides? - Rectangle and circle

The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long. - Thales

Calculate the length of the Thales' circle described to right triangle with hypotenuse 18.4 cm. - Trees

Loggers wanted to seed more than 700 and less than 800 trees. If they seed in rows of 37, left them 8 trees. If they seed in rows of 43, left the 11 trees. How many trees must seed ? - Tent

Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m. - Machines 2

2 machines for 50 hours produces 2,000 products. How many machines need to buy to make in 30 hours 15,000 products? - Chord MN

Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle. - Rectangle

The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle. - Clocks

How long track travel the second hand in 46 hours, the end of which is 4 cm long. - Deposit 3

After a year had Martin on bank account € 2028. What was the interest rate when the initial deposit was € 1879? - Circular flowerbed

Circular flowerbed with diameter 8 m we split by concentric circle to circle and annulus with the same area. Determine the radius of the circle. - 10 pieces

How to divide the circle into 10 parts (geometrically)? - Bottle

Bottle with wine costs 58 USD. Wine is 27 USD more expensive than the empty bottle. How much is the bottle itself? - Rectangular trapezoid

Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC. - Friends

Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends? - Total displacement

Calculate total displacement of the 4-cylinder engine with the diameter of the piston bore B = 6.6 cm and stroke S=2.4 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back. - Olympics

In how many ways can be placed 6 athletes on the podium at the Olympics? Depend on the color of the metal. - The dice

What is the probability of events that if we throw a dice is rolled less than 6?

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