# 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. Circle and hexagon Calculate the radius of a circle whose circumference is 8.4 cm longer than the circumference of the inscribed regular hexagon.
2. Surveyor Calculate the area of ​​what may vary rectangular, if it focused by surveyor and found the dimensions 18 x 15 m while in each of the four joint points can be position deviation 25 cm?
3. Harvester Harvester has cutting width 4 m and harvested grain in the field, which is 87 meters wide. Harvester moves along the length of the field for six minutes, going back (without cutting) it takes half the time. Each turn at the end field take one minute. How m
4. MO-Z5-3-66 tiles The picture shows a square tiles with side 10 dm which is composed of four identical small rectangles and squares. Circumference of small square is five times smaller than the circumference of the entire tile. Determine the dimensions of the rectangle.
5. CD disc A compact disc has a diameter of 11.8 cm. What is the surface area of the disc in square centimeters?
6. Moivre 2 Find the cube roots of 125(cos 288° + i sin 288°).
7. High wall I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
8. Wall painting The wall is 5 meters wide and 2 meters high. Window in the wall has dimensions 2x1,8 meters. How many litera of color is needed to paint two-layer this walls, if the 1 m2 needs 1.1 liters of paint?
9. Circle What is the radius of the circle whose perimeter is 6 cm?
10. Parallelogram ABCD The area of parallelogram ABCD is 440 cm2. Points M and N are the midpoints of the sides AB and BC. What is the area of a quadrilateral MBND?
11. Alfa beta gama The triangle's an interior angle beta is 10 degrees greater than the angle alpha and gamma angle is three times larger than the beta. Determine the size of the interior angles. The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)?
13. Chord 4 I need to calculate the circumference of a circle, I know the chord length c=22 cm and the distance from the center d=29 cm chord to the circle.
14. Internal and external angles Calculate the remaining internal and external angles of a triangle, if you know the internal angle γ (gamma) = 34 degrees and one external angle is 78 degrees and 40 '. Determine what kind of triangle it is from the size of its angles.
15. Square Draw a square on the edge of a = 4 cm. Mark the center of symmetry S and all axes of symmetry. How many axes of symmetry does? Write down.
16. Strip From 5.9 cm wide strip should be cut rhombus with area 28 cm2. How long will be its side?
17. Roof Tiles are stacked in rows on the trapezoidal shaped roof. At the ridge is 15 tiles and each subsequent row has one more tile than in the previous row. How many tiled is covered roof if lowermost row has 37 tiles?
18. Tiles How much you will pay CZK for laying tiles in a square room with a diagonal of 8 m if 1 m2 cost CZK 420?
19. Isosceles triangle Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.
20. Rhombus PQRS is a rhombus. Given that PQ=3 cm & height of rhombus is given 2 cm. Calculate its area.

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