# 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. N-gon How many diagonals has convex 11-gon?
2. Circular sector I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?
3. Euclid2 In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
4. Tiles Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled and how many we need them?
5. Circle in rhombus In the rhombus is inscribed circle. Contact points of touch divide the sides to parts of length 19 cm and 6 cm. Calculate the circle area.
6. Sea How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km).
7. Garden plot Calculate how many meters of fence need to fence the square garden with length and width of 22 meters.
8. Garden How many steps of 76 cm circumvent square garden with area 1.8 ha?
9. Circle Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
10. Trapezoid trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
11. The bridge Across the circle lakepasses through its center bridge over the lake. At three different locations on the lake shore are three fishermen A, B, C. Which of fishermen see the bridge under the largest angle?
12. MO circles Juro built the ABCD square with a 12 cm side. In this square, he scattered a quarter circle that had a center at point B passing through point A and a semicircle l that had a center at the center of the BC side and passed point B. He would still build a ci
13. Triangle KLB It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o
14. Cathethus and the inscribed circle In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
15. Do you solve this? Determine area S of rectangle and length of its sides if its perimeter is 102 cm.
16. Distance Calculate distance between two points X[18; 19] and W[20; 3].
17. Circumscribing Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
18. Glass mosaic How many dm2 glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%.
19. Rectangle A2dim Calculate the side of the rectangle, if you know that its area is of 2590 m2 and one side is 74 m.
20. Inscribed rectangle The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...