# Planimetrics - problems - page 52

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. If the
If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
2. Tv screen
The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen?
3. Calculate
Calculate the length of a side of the equilateral triangle with an area of 50cm2.
4. The sides
The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
5. KLMN trapezoid
The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?
6. Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
7. Rectangle diagonal
The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2.
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
9. RT - inscribed circle
In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
10. The swimmer
The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motion
11. SSA and geometry
The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
12. Rectangles
How many different rectangles with sides integers (in mm) have a circumference exactly 1000 cm?
13. Square
Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?
14. Equation - inverse
Solve for x: 7: x = 14: 1000
15. Rectangle - area, perimeter
The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
16. Square into three rectangles
Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
17. Inscribed rectangle
What is the perimeter of a rectangle that is inscribed in a circle whose diameter is 5 dm long? Answer: 14 dm
18. Waste
How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
19. Three segments
The circle is divided into 3 segments. Segment A occupies 1/4 of the area, segment B occupies 1/3 of the area. What part is occupied by section C? In what proportion are areas A: B: C?
20. Right triangle
Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?

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