# 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. Circles Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?
2. Ratio of perimeters Rectangle ABCD has dimensions 3 cm and 4 cm, KLMN rectangle has dimensions 4 cm and 12 cm. Calculate the ratio of the perimeter ABCD and perimeter KLMN.
3. Do you solve this? Determine area S of rectangle and length of its sides if its perimeter is 102 cm.
4. 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.
5. The carpet How many meters of carpet 90 cm wide need to cover floor room which has a rectangular shape with a lengths 4.8 m and 2.4 m if the number of pieces on the carpet is needed to be lowest?
6. Rectangle The rectangle area is 182 dm2, its base is 14 dm. How long is the other side? Calculate its perimeter.
7. Goat and circles What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which
8. Building The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
9. ISO Triangle V2 Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
10. Tree How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
11. Wheel Diameter of motocycle wheel is 52 cm. How many times rotates wheel on roand long 2 km?
12. Wheel What is the wheel diameter if on the 0.38 km track turns 128 times?
13. ISO trapezoid v2 bases of Isosceles trapezoid measured 12 cm and 5 cm and its perimeter is 21 cm. What is the are of a trapezoid?
14. Acute angles Sizes of acute angles in the right-angled triangle are in the ratio 1: 3. What is size of the larger of them?
15. Climb in percentage The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km.
16. Parallelogram The perimeter of the parallelogram is 417 cm. The length of one side is 1.7-times longer than the length of the shorter side. What is the length of sides of a parallelogram?
17. Square ABCD Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
18. 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?
19. Plan of the village Plan of the municipality in 1:1000 scale has plotted garden with dimensions 25 mm and 28 mm. Determine the area of gardens in ares in reality.
20. Glass Peter broke the window glass with size 110 cm and 90 cm. 1 square meter of glass costs 11 USD. How much money is need to pay for a new glass?

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

We will send a solution to your e-mail address. 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...