# 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. Median The median of the triangle LMN is away from vertex N 84 cm. Calculate the length of the median, which start at N.
2. Triangle Calculate the area of right triangle ΔABC, if one leg is long 14 and its opposite angle is 59°. Ladder 6.4 meters long is positioned in the well such that its lower end is distanced from the wall of the well 1.2 m. The upper part of the ladder is supported on the upper edge of the well. How high is the well?
4. Similarity ABC is a triangle wherein a = 4 cm, b = 6 cm, c = 8 cm. Is it similar to the triangle DEF: d = 3 cm, e = 4.5 cm, f = 6 cm? If so, determine the ratio of similarity.
5. Isosceles trapezoid Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
6. Gardens colony Gardens colony with dimensions of 180 m and 300 m are to be completely divided into the same large squares of the highest area. Calculate how many such squares can be obtained and determine the length of the square side.
7. Trapezoid How long are the trapezoid bases with area 24 cm2 and height 3 cm. One base is 3 times longer than the shorter.
8. Potatoes When planting potatoes there are consumed 230 kg of seed per 1 ha. Calculate the weight of the seed needed for fitting a square area with a side length 325 meters.
9. Squares Calculate the area of square and result round to square decimeters. a) a = 1,52 dm b) a = 13 268mm c) a = 562 cm d) a = 1,52 m
10. Circle and rectangle A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.
11. Triangle - is RT? Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, side c is 31 cm longer than side a. Calculate the length of sides and determine whether triangle is a right triangle.
12. Land Land has a rectangular shape, its surface area is 1.45 hectares. Its width is 250 m. Determine the length of the land.
13. Outer angles The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertx B is 136°50'. What size has the inner triangle angle at the vertex C?
14. Well Rope with a bucket is fixed on the shaft with the wheel. The shaft has a diameter 50 cm. How many meters will drop bucket when the wheels turn 15 times?
15. Trapezium The length of the base and the height size of the base of the trapezium is at ratio 5:3:2, the content area of the trapezium is 128 cm2. Calculate the length of the base and the height of the trapezoid.
16. Diagonals Draw a square ABCD whose diagonals have a length of 6 cm
17. Isosceles trapezoid In an isosceles trapezoid KLMN intersection of the diagonals is marked by the letter S. Calculate the area of trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm2.
18. Triangle ABC In a triangle ABC side b measure 10 cm less than the side a and side b is half of the side c. Calculate the length of sides if the circumference of the triangle is 42 cm.
19. Is right? Determine whether the triangle with legs (catheti) 19.5 cm and 26 cm and length of the hypotenuse 32.5 cm is rectangular?
20. Triangle midpoints Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.

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