# 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. Rectangles How many different rectangles with sides integers (in mm) have a circumference exactly 1000 cm?
2. Rectangle - area, perimeter The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
3. Waste How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
4. Inscribed rectangle What is the perimeter of a rectangle that is inscribed in a circle whose diameter is 5 dm long? Answer: 14 dm
5. Square into three rectangles Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
6. Three segments The circle is divided into 3 segments. Segment A occupies 1/4 of the area, segment B occupies 1/3 of the area. What part is occupied by section C? In what proportion are areas A: B: C?
7. Right triangle Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?
8. Depth angle From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
9. One hectare How many square meters are one hectare?
10. A truck A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
11. Circle simple Circumference of a circle is 6.28. What is the area of the circle?
12. Perimeter of square The square has a circumference 17cm. What is its area?
13. Velocipedes In the 19th century, bicycles did not have a chain drive, and the pedals were connected directly to the wheel axis. This wheel diameter gradually increased until the so-called high bicycles (velocipedes) with a front wheel diameter of up to 1.5 meters, whi Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder?
15. Pavement Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
16. An angle An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x.
17. Special watch Fero bought a special watch on the market. They have only one (minute) hand and a display that shows which angle between the hour and minute hand. How many hours it was when his watch showed - the minute hand points to number 2; the display shows 125°?
18. Three points Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
19. Hexagon ABCDEF In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
20. Three sides Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. .

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