# 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. Find the 12 Find the equation of the circle with center (3,7) and circumference 8π units.
2. The aspect ratio The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.
3. The schoolyard The schoolyard had the shape of a square with an 11m side. The yard has been enlarged by 75 m2 and has a square shape again. How many meters was each side of the yard enlarged?
4. Eq triangle minus arcs In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
5. Mysterious area The trapezoid ABCD is given. Calculate its area if the area of the DBC triangle is 27 cm2.
6. Playground The land for the construction of the school playground has the shape of a rectangle with a shorter side of 370 m. Its other side is 260 m longer. How many meters of the fence does the school need to buy on the fencing playground?
7. Two patches Peter taped the wound with two rectangular patches (one over the other to form the letter X). The area sealed with both patches at the same time had a content of 40cm2 and a circumference of 30cm. One of the patches was 8cm wide. What was the width of t
8. Tiles The rectangular floor of the 6 x 1.8 m dimensions is to be covered with 50 cm square tiles. How many tiles will be needed?
9. The perimeter of the rectangle The length, l, of a rectangle is 4 inches greater than its width, w. The perimeter of the rectangle is at least 30 inches. What inequality shows the range of possible widths of the rectangle?
10. Tablecloths The restaurant has sixty-two square tablecloths with a side length of 150 cm and 36 rectangular tablecloths with dimensions of 140 cm and 160 cm. A) How many meters of hemming ribbon will be needed if we add 50 cm to each tablecloth? B) The ribbon sale
11. The parabolic segment The parabolic segment has a base a = 4 cm and a height v = 6 cm. Calculate the volume of the body that results from the rotation of this segment a) around its base b) around its axis.
12. Paint cans How many paint cans do we need to paint the floor in two rooms with dimensions of 6.8m x 4.5m and 6m x3.8m? One can arefor 6m².
13. Median in right triangle In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
14. Rectangles Vladimir likes to draw rectangles. Yesterday he created all rectangles that had sides in centimeters and a circumference of 18 cm. How many rectangles of different dimensions have been drawn?
15. Irregular pentagon A rectangle-shaped, 16 x 4 cm strip of paper is folded lengthwise so that the lower right corner is applied to the upper left corner. What area does the pentagon have?
16. Picture frames Destiny has to make 24 picture frames. Each frame uses 16 3/8 wood trim. 2/3 were completed on the first day. How many inches of wood trim is needed to complete the remaining frames on the second day?
17. Rectangles How many different rectangles can be made from 60 square tiles of 1 m square? Find the dimensions of these rectangles.
18. Two circles Two circles with the same radius r = 1 are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles?
19. Construct rhombus Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm
20. Rectangular garden The perimeter of Peter's rectangular garden is 98 meters. The width of the garden is 60% shorter than its length. Find the dimensions of the rectangular garden in meters. Find the garden area in square meters.

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