# Planimetrics - problems - page 44

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. Diagonal of square
Calculate the side of a square when its diagonal is 10 cm.
2. Rhombus sides
find the sides of a rhombus, it area is 550 cm square and altitude is 55cm
3. Diagonals
Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.
4. Scalene triangle
Solve the triangle: A = 50°, b = 13, c = 6
5. Find the area
Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft
6. Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta
7. Resultant force
Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
8. Two lands
The common area of the two neighboring lands is 964 m2. The second land is 77 m2 smaller than twice the size of the first land. Find the areas of each land.
The ladder has a length 3.5 meters. He is leaning against the wall so that his bottom end is 2 meters away from the wall. Determine the height of the ladder.
10. Chord
It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
11. Forces on earth directions
A force of 60 N [North] and 80 N [East] is exerted on an object wigth 10 kg. What is the acceleration of the object?
12. Hexagon area
The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area.
13. Ratio iso triangle
The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.
14. Parallelogram
Calculate the missing side of a parallelogram, if you know the perimeter o and one side: a) o = 7.2 cm; b = 1.8 cm b) o = 5.4 cm; a = 1.9 cm
15. Trapezium ABCD
In the figure, ABDC is a trapezium in which AB || CD. line segments RN and LM are drawn parallel to AB such that AJ=JK=KP. If AB=0.5m and AP=BQ=1.8m, find the lengths of AC, BD, RN and LM. angle D=angle C=60
16. Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
17. Diameter
The diameter of a circular plot is 14 dm. Find the circumference and area.
18. Parallelogram perimeter
The ABC triangle with sides a = 5cm, b = 3cm, c = 40mm has the center of the sides of the K,L,M. How many cm have the KBLM parallelogram perimeter?
19. Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
20. Bicycle wheel
After driving 157 m bicycle wheel rotates 100 times. What is the radius of the wheel in cm?

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