Planimetrics - problems - page 35

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

1. Magic belt The magic rectangular belt has the property that whenever its owner wants something, the length of the belt is reduced to 1/2 and the width to 1/3. After three such wishes, the belt had a content area 4 cm2. What was its original length if the original wid
2. Playground Fencing square playground cost € 464; 1 meter cost € 19. What is the area of the playground?
3. Angles in triangle Calculate the alpha angle in the triangle if beta is 61 degrees and 98 gamma degrees.
4. The sum graphically Draw a graphically sum of the all sides of 4-gon ABCD.
5. Rectangle 3-4-5 The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
6. Triangle KLM In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm
7. Clock Tower What angle is betwenn hands on Clock Tower when show 17 hours and 35 minutes?
8. Interesting property Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle?
9. Rectangle The rectangle area is 182 dm2, its base is 14 dm. How long is the other side? Calculate its perimeter.
10. Annulus Calculate the area of two circles annulus k1 (S, 3 cm) and k2 (S, 5 cm).
11. Triangle Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201
12. The mast A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
13. Medians and sides Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
14. Triangle ABC v2 Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
15. Math heart Stylized heart shape created from a square with side 5 cm and two semicircles over his sides. Calculate the content area and its circumference.
16. Angle Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.
17. Isosceles trapezoid v3 In an isosceles trapezoid ABCD is the size of the angle β = 81° Determine size of angles α, γ and δ.
18. V-belt Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
19. The farmer The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine th
20. Right triangles How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality).

Do you have an interesting mathematical problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.