# 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. Arc Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle?
2. Laws From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
3. Similarity Are two right triangles similar to each other if the first one has a acute angle 70° and second one has acute angle 20°?
4. Described Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
5. Medians Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
6. Kites Boys run kite on a cable of 68 meters long. What is the kite altitude, if the angle from the horizontal plane is 72°?
7. Trapezoid Calculate area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm..
8. Infinity In a square with side 18 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares. Ladder 8 m long is leaning against the wall. Its foot is 1 m away from the wall. In which height ladder touches the wall?
10. Rectangle SS Perimeter of a rectangle is 268 cm and its diagonal is 99.3 cm. Determine the dimensions of the rectangle.
11. R Trapezium Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
12. Arc and segment Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
13. Triangle Can be rectangular triangle equilateral?
14. Angles Determine the interior angles of a rhombus with area 319.1 cm2 and perimeter 72 cm.
15. Mr. Zucchini Mr. Zucchini had a rectangular garden whose perimeter is 28 meters. Content area of the garden filled just four square beds, whose dimensions in meters are expressed in whole numbers. Determine what size could have a garden. Find all the possibilities and
16. Quarter circular The wire that is hooked around the perimeter of quarter-circular arc has length 3π+12. Determine the radius of circle arc.
17. Octagon We have a square with side 84 cm. We cut the corners to make his octagon. What will be the side of the octagon?
18. Hexagon There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
19. Rhombus Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm.
20. Triangle SSS Calculate perimeter and area of ​​a triangle ABC, if a=42, b=57 and c=42.

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