# 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. Chors centers The circle with a diameter 17 cm, upper chord /CD/ = 10.2 cm and bottom chord /EF/ = 7.5 cm. The midpoints of the chords H, G is that /EH/ = 1/2 /EF/ and /CG/ = 1/2 /CD/. Determine the distance between the G and H, if CD II EF (parallel).
2. Rectangle The length of one side of the rectangle is three times the length of the second side. What are the dimensions of the rectangle if its circumference 96 cm?
3. Carpet What is the price of square carpet side length 3.25 m if one meter square cost 230 CZK?
4. Ethernet cez ulicu Karol a Jozef sú vášniví hráči počítačových hier a býva v domoch, ktoré sú presne naproti sebe cez ulicu, takže si vidia navzájom do okien. Rozhodli sa, že si svoje počítače prepoja telefónnym káblom aby mohli hrať spoločne hry. Karol býva v prvom poschodí
5. Medians and sides Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
6. 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
7. Playground Fencing square playground cost € 464; 1 meter cost € 19. What is the area of the playground?
8. The sum graphically Draw a graphically sum of the all sides of 4-gon ABCD.
9. Angles in triangle Calculate the alpha angle in the triangle if beta is 61 degrees and 98 gamma degrees.
10. 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.
11. 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
12. Clock Tower What angle is betwenn hands on Clock Tower when show 17 hours and 35 minutes?
13. 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?
14. Rectangle The rectangle area is 182 dm2, its base is 14 dm. How long is the other side? Calculate its perimeter.
15. Annulus Calculate the area of two circles annulus k1 (S, 3 cm) and k2 (S, 5 cm).
16. 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
17. 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.
18. 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.
19. 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.
20. 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.

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