# Planimetrics - math word problems

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. Children playground The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
2. Diagonals What x-gon has 54 diagonals?
3. The pole The telegraph pole is supported by a 4 m bullet at 3/4 of its height, the end of which is at a distance 2.5 m from the pole post. Calculate the height of the telegraph pole.
4. Trapezium 2 Trapezium has an area of 24 square cms. How many different trapeziums can be formed ?
5. Hyperbola Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
6. Pendulum Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm.
7. Clock hands The second hand has a length of 1.5 cm. How long does the endpoint of this hand travel in one day?
8. Vertices of a right triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle. From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes?
10. Rhombus 29 One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus.
11. Sum of squares The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
12. Pravoúhly trojúhelník Určete obsah pravoúhlého trojúhelníku, jehož délky stran tvoří po sobě jdoucí členy aritmetické posloupnosti a poloměr kružnice opsané tomuto trojúhelníku je 5 cm.
13. Isosceles triangle The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
14. A trapezoid A trapezoid 75 ft wide on top 85 ft on the bottom, the height is 120 ft. What is its area in the square yds?
15. Right angled triangle 3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
16. Scale of plan On the plan of the village in the scale of 1: 1000 a rectangular garden is drawn. Its dimensions on the plan are 25mm and 28mm. Determine the area of the garden in ares.
17. Rectangle There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
18. RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
19. Table Find the circumference of the table, where the long side is 1.28 meters and the short side is 86 cm.
20. Tangent 3 In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.

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