# Examples for 9th grade - page 21

- Trapezoid MO-5-Z8

ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm^{2}. Determine the area of the trapezoid A - Rectangle diagonals

It is given rectangle with area 24 cm^{2}a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers. - Sales vs profit

Apple sells 22 percent less computes than the Acer but the profit from their sales is 2.2 times higher than Acer. How many times are Apple computer more expensive than Acer? - Axial section

Axial section of the cylinder has a diagonal 40 cm. The size of the shell and the base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder. - Euler problem

Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels? - Felix

Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km. - Sphere growth

How many times grow volume of sphere if diameter rises 10×? - Circumferential angle

Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9. Determine the size of the angles of the triangle ΔABC. - Water container

Container with water weighs 1.48 kg. When we cast 75% of water container of water weight 0.73 kg. How heavy is an empty container? - Two workers

Two workers together execute some work in 10 days. The first worker would have done himself in 20 days. How many days would have done himself a second worker? - Segments

Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide? - 9.A

9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5? - Dog

Man goes with a dog on a long walk 17 km from the house. Man is walking at speed 4.9 km/h and a dog that constantly running between house and man at 12.6 km/h. How many kilometers will run the dog when they reach their destination? - Isosceles III

The base of the isosceles triangle is 17 cm area 416 cm^{2}. Calculate the perimeter of this triangle. - Circles

Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square? - Rectangle

Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle? - Pizza

A school survey found that 12 out of 15 students like pizza. If 6 students are chosen at random, what is the probability that all 6 students like pizza? - Cuboid

Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees). - Bits, bytes

Calculate how many different numbers can be encoded in 16-bit binary word? - Right triangle

Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.

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