# 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. Circumference - a simple What is the ratio of the circumference of any circle and its diameter? Write the result as a real number rounded to 2 decimal places.
2. Area 4gon Calculate area of 4-gon, two and the two sides are equal and parallel with lengths 11, 5, 11 and 5. Inner angles are 45°, 135°,45°, 135°.
3. Squaring the Circle Calculating side of the square with the same area as the circle of radius 18.
4. ISO Triangle V2 Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
5. Square side Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
6. Triangle Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33. Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
8. Similarity of squares The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ?
9. Triangle Prove whether you can construct a triangle ABC, if a=9 cm, b=6 cm, c=10 cm.
10. Again saw From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 146 mm and 128 mm. What is the trunk smallest diameter?
11. Clock What distance will pass end of 8 cm long hour hand for 15 minutes?
12. Gon functions Decide which of the numbers (values ​​of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1. 8.3 meters long ladder is leaning against the wall of the well, and its lower end is 1.2 meters from this wall. How high from the bottom of a well is the top edge of the ladder?
14. Isosceles trapezoid Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid.
15. Snowman In a circle with a diameter 50 cm are drawn 3 circles /as a snowman/ where: its diameters are integers, each larger circle diameter is 3 cm larger than the diameter of the previous circle. Determine snowman height if we wish highest snowman.
16. Rectangular triangles The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 c What size have angles in quadrilateral (4-gon) if they are in a ratio of 8: 9: 10: 13?
18. Shape Plane shape has a maximum area 677 mm2. Calculate its perimeter if perimeter is the smallest possible.
19. Diagonal Can be a diagonal of diamond twice longer than it side?
20. Minute-hand How long distance will travel a large (minute) hand on the clock for 47 minutes, if its length is 43 cm?

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