# 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. Trapezoid MO-5-Z8 ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A
2. Map Forest has an area of ​​36 ha. How much area is occupied by forest on the map at scale 1:500?
3. Shooter The probability that a good shooter hits the center of the target circle I is 0.1. The probability that the target hit intercircle is II 0.58. What is the probability that it hits the target circle I or II?
4. Rectangle diagonals It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
5. Circumferential angle Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9. Determine the size of the angles of the triangle ΔABC. Road sign informs the gradient is 10.3%. Calculate the angle which average decreases.
7. 3-bracket May be the largest angle in the triangle less than 20°?
8. Intersections How many intersections have circles with radius 16 mm and 15 mm, if the distance of their centers is 16 mm.
9. Gardens The garden has the square shape with circumference 124 m. Divide it into two rectangular gardens, one should circumference 10 meters more than the second. What size will have a gardens?
10. Circles Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?
11. Right triangle Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
12. Tiles The room has dimensions 12 m and 5.6 m. Determine the number of square tiles and their largest possible size to cover them room's floor.
13. Isosceles III The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
14. N-gon angles What is the sum of interior angles 8-gon? What is the internal angle of a regular convex 8-polygon?
15. Rectangle Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
16. Garden The garden has two opposite parallel fences. Their distance is 33.1 m. Lengths in these two fences are 75.5 meters and 49.4 meters. Calculate the area of this garden. Calculate the radius of the quadrant, which area is equal to area of circle with radius r = 15 cm.
18. Boat A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight?
19. Similarity n-gon 9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S1=190 dm2 and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm.
20. Rhombus HP Calculate area of the rhombus with height 24 dm and perimeter 12 dm.

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