# 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 - TS v2 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
2. The carpet How many meters of carpet 90 cm wide need to cover floor room which has a rectangular shape with a lengths 4.8 m and 2.4 m if the number of pieces on the carpet is needed to be lowest?
3. The book The book has 280 pages. Each side is a rectangle with sides 15 cm and 22 cm. a) how many leaves has the book? b) at least how many square meters of paper should be used to production this book?
4. RT and circles Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
5. Wheels Small tractor wheel with a diameter of 60 cm must be rotated 8 times to overcome some pathway. How many times must turn the big tractor wheel with a radius 60 cm to overcome the same distance?
6. Tiles How many 46 cm square tiles will cover a floor 22.08 m by 8.74 m?
7. Flywheel Flywheel turns 450 rev/min (RPM). Determine the magnitude of the normal acceleration of the flywheel point which are at a distance of 10 cm from the rotation axis.
8. Rectangle Anton Difference between length and width of the rectangle is 8. Length is 3-times larger than the width. Calculate the dimensions of the rectangle.
9. Round table tablecloth Round table has area 50.24 dm2. Calculate the diameter of the circular tablecloth, if it is extend beyond the edge of the table by 30 cm.
10. Parcel Both dimensions of the rectangular parcel were increased by 26%. By how many % has increased its acreage?
11. RT 10 Area of right triangle is 84 cm2 and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC.
12. Silo Outer perimeter of silo is 32 m. Concrete wall is 35 cm thick. What is diameter and area of inside floor of silo?
13. Ratio - rectangle The rectangle has dimensions 6 cm and 9 cm. How many times increases area and its perimeter, when its dimensions increase in the ratio 5:3?
14. Medians in triangle Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm.
15. Right angled triangle 2 LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n
16. Sails We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
17. Triangle ABC Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
18. Right triangle - leg Calculate to the nearest tenth cm length of leg in right-angled triangle with hypotenuse length 9 cm and 7 cm long leg.
19. Tangents construct Circle is given k (S; 2.5 cm) and an outer line p. Construct a tangent t of the circle that has with a line p angle 60°. How many solutions has the task?
20. Center of gravity In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.

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