# 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. 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.
2. Rectangle The width of the rectangle is 65% of its length. Perimeter of the rectangle is 132 cm. Determine the dimensions of the rectangle.
3. Internal angles The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Det
4. 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
5. 3x square Side length of the square is 54 cm. How many times increases the content area of square if the length of side increase three times?
6. Pavilion The rectangular pavilion with dimensions 3.5 m and 2.75 m to be paved with square tiles of side 25 cm price of CZK 22 per 1 piece or rectangular tiles with sides of 20 cm and 15 cm in the price of CZK 11 per 1 pc. Which solution is cheaper (write its pric
7. Square Calculate the side of a square with a diagonal measurement 10 cm.
8. Chord circle The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
9. Umbrella Can umbrella 75 cm long fit into a box of fruit? The box has dimensions of 390 mm and 510 mm.
10. Area of square Calculate the content area of the square whose perimeter is 24 dm.
11. Park In the park is marked diamond shaped line connecting locations A, D, S, C, B, A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m.
12. MO - triangles On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB s
13. Acreage What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ?
14. Dog Dog is tied to a chain, which is mounted in a corner of the yard. Yard has the shape of a square with a side length of 20 meters. The same long is also dogchain. Are there places in the yard where dog can't reach?
15. Glass At the glass shop we have to cut 8 sheets of glass. Each was shaped a square with sides of 18 cm. We paid 44 CZK. How much is a 1 m2 of glass?
16. Trio 2 Decide whether trio of numbers is the side of a right triangle: 26,24,10.
17. Rhombus 4 Circumference of the rhombus is 44 cm, its height is 89 mm long. Calculate its content area.
18. Hypotenuse Calculate the length of the hypotenuse of a right triangle with a catheti 71 cm and 49 cm long.
19. Parallelogram In the parallelogram we know one internal angle 67°33`. Calculate the other internal angles.
20. Length IT Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm

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