# 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. 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.
2. Lawns Before a sports hall are two equally large rectangular lawns, each measuring 40 m and 12 m. Maintenance of 10m² lawn cost 45 CZK yearly. On each lawn is circular flowerbed with a diameter 8 meters. How much money is needed each year to take on lawn care?.
3. Hypotenuse Calculate the length of the hypotenuse of a right triangle with a catheti 71 cm and 49 cm long.
4. Circle - simple The circumference of a circle is 930 mm. How long in mm is its diameter?
5. Angles in ratio The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z.
6. Acreage Plot has a diamond shape, its side is 25.6 m long and the distance of the opposite sides is 22.2 meters. Calculate its acreage.
7. Garden The garden has a rectangular shape with lengths of 25 and 40 meters. It has been expanded so that each of its size increased by one fifth. How many square meters increased its acreage? The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
9. Forces Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
10. Two circles Two circles with a radius 4 cm and 3 cm have a center distance 0.5cm. How many common points have these circles?
11. Ace The length of segment AB is 24 cm and the point M and N divided it into thirds. Calculate the circumference and area of this shape.
12. 22/7 circle Calculate approximately area of a circle with radius 20 cm. When calculating π use 22/7.
13. Kite John a kite, which is diamond shaped. Its diagonals are 60 cm long and 90 cm long. Calculate: a) the diamond side b) how much paper John needs to make a kite if he needs paper on both sides and needs 5% of the paper for bending.
14. Midpoints Triangle ABC with sides a = 5 cm, b = 3 cm, c = 40mm has a midpoint of K, L, M. How many centimeters is long perimeter of parallelogram KBLM?
15. Circle r,D Calculate the diameter and radius of the circle if it has length 52.45 cm.
16. Odometer The odometer is driven by rotation of the wheel whose diameter is 65 cm. After how many rotations the wheel turns counter to next kilometer?
17. Circle's chords In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.
18. Diagonals of a rhombus One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.
19. Diamond perimeter Calculate the diamond circumference which area is 288 cm square and one diagonal has a size of 124 cm.
20. Internal angles Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at the vertex A.

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