# 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. Points on circle In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are i
2. Square and rectangle Calculate the side of a square which content area equals area of the rectangle having a length of 3 cm greater and by 2 cm smaller than the side of the square.
3. Tiles path A rectangular park measures 24mX18m. A path 2.4m wide is constructed all around it. Find the cost of paving the path with cement tiles of size 60cm X 40cm at the rate of \$5.60 per tile ?
4. MO8-Z8-I-5 2017 Identical rectangles ABCD and EFGH are positioned such that their sides are parallel to the same. The points I, J, K, L, M and N are the intersections of the extended sides, as shown. The area of the BNHM rectangle is 12 cm2, the rectangle MBCK area is 63.
5. Largest angle of the triangle What is the largest angle of the triangle if the second angle is 10° greater than twice the first and the third is 30° smaller than the second?
6. Sunflower Field The trapezoidal sunflower field is located between two parallel paths which are spaced 230 meters apart. The lengths of the parallel sides of the field are 255 m and 274 m. How many tons of sunflower will come from this field if the hectare yield is 2.25.
7. 30-gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
8. Perimeter from area What is the perimeter of the square if its content is 64 cm2?
9. Ballistic curve The ballistic grenade was fired at a 45° angle. The first half ascended, the second fall. How far and how far it reached if his average speed was 1200km/h, and 12s took from the shot to impact.
10. Flowerbed In the park there is a large circular flowerbed with a diameter of 12 m. Jakub circulated him ten times and the smaller Vojtoseven times. How many meters each went by and how many meters did Jakub run more than Vojta?
11. Rhombus 4 Circumference of the rhombus is 44 cm, its height is 89 mm long. Calculate its content area.
12. 3x square Side length of the square is 54 cm. How many times increases the content area of square if the length of side increase three times?
13. Diagonal of the rectangle Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.
14. Circle from string Martin has a long 628 mm string . He makes circle from it. Calculate the radius of the circle.
15. Disc Circumference of the disk is 78.5 cm. What is the circumference of the circular arc of 32° on the disc?
16. Two diagonals The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal?
17. Flowerbed Family cultivated tulips on a square flower bed of 6 meters. Later they added the square terrace with a side of 7 meters to their house. One vertex of the terrace lay exactly in the middle of a tulip bed, and one side of the terrace divided the side of the
18. Square Calculate the side of a square with a diagonal measurement 10 cm.
19. Circle - simple Calculate the area of a circle in dm2, if its circumference is 31.4 cm.
20. Trapezoid MO-5-Z8 Trapezoid KLMN has bases 12 and 4 cm long. The area of triangle KMN is 9 cm2. What is the area of the trapezoid KLMN?

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