# Examples for 8th grade

- Sun rays

If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current he - In the orchard

In the orchard, they planted 25 apple trees, 20 pears, 15 plums and 40 marbles. A strong late frost, however, destroyed a fifth of all new trees. Unfortunately, it was all the trees of one kind of fruit. What is the probability that the plums have died ou - Syringe and patient

In 1 ampoule of 2 ml is 15 mg of Dipidol. The patient should receive 10 mg. How much ml do I draw into the syringe? - Steamer

At 6 hours 40 minutes steamer sailed from the port at speed 12 km/h. At exactly 10 hours started sail motorboat at speed 42 km/h. When motorboat will catch steamer? - Isosceles right triangle

Contents of an isosceles right triangle is 18 dm^{2}. Calculate the length of its base. - Trapezoid thirds

The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment. - Rectangle

Find the dimensions of the rectangle, whose perimeter is 108 cm and the length is 25% larger than the width. - Real estate

Residential house has three entrances numbered by odd numbers arithmetic progression. The sum of the two numbers on the corner entrances is 50. Calculate the highest of this three numbers. - Diagonals

Draw a square ABCD whose diagonals have a length of 6 cm - Equilateral triangle

The equilateral triangle has a 23 cm long side. Calculate its content area. - Trees

Along the road were planted 250 trees of two types. Cherry for 60 CZK apiece and apple 50 CZK apiece. The entire plantation cost 12,800 CZK. How many was cherries and apples? - Potatoes 6

The farmer brought potatoes to the market. In the first hour he sold two-fifths of the potatoes brought, in the second hour he sold five-sixth of the remaining potatoes, and in the third hour he had sold the last 40kg of potatoes. How many kg of potatoes - Double ladder

The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart? - Rhombus

If we increase the rhombus side by 2.4 cm; its perimeter is 20 cm. How long was the side of the rhombus? - Isosceles triangle

Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm. - Empty canister

The canister is filled with oil weight 17 kg. If filled only half weight 9 kg. What weight does my empty canister have? - Square

Calculate the perimeter and the area of square with a diagonal length 30 cm. - Billboard

Rectangular billboard is 2.5 m long with a diagonal 2.8 m long. Calculate the perimeter and the content area of the billboard. - Land - isosceles trapezoid

Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m. - Workers

Group of workers washing half of the windows of the building in two hours. How long will take half the workers wash all the windows of the building?

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