# 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.- 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 cm^{2}. What was its original length if the original wid - Playground

Fencing square playground cost € 464; 1 meter cost € 19. What is the area of the playground? - Angles in triangle

Calculate the alpha angle in the triangle if beta is 61 degrees and 98 gamma degrees. - The sum graphically

Draw a graphically sum of the all sides of 4-gon ABCD. - 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. - 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 - Clock Tower

What angle is betwenn hands on Clock Tower when show 17 hours and 35 minutes? - 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? - Rectangle

The rectangle area is 182 dm^{2}, its base is 14 dm. How long is the other side? Calculate its perimeter. - Annulus

Calculate the area of two circles annulus k_{1}(S, 3 cm) and k_{2}(S, 5 cm). - 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 - 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. - 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. - 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. - 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. - Angle

Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence. - Isosceles trapezoid v3

In an isosceles trapezoid ABCD is the size of the angle β = 81° Determine size of angles α, γ and δ. - 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 - 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 - 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).

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