# 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. Equator Suppose that tourist went on foot over the Globe equator. How many meters more track made ​​his hat on his head as the shoes on your feet? The radius of the earth is 6378 km and height of the tourist is 1.7 m.
2. Acute angles Sizes of acute angles in the right-angled triangle are in the ratio 1: 3. What is size of the larger of them?
3. 3d vector component The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
4. Isosceles IV In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
5. Tablecloth The table top is 90 cm long and 50 cm wide. How many cm lace edging is necessary for the tablecloth that hangs on each side by 10 cm?
6. Arc What area of a circle occupied the flowers planted in the arc of a circle with radius 4 m with central angle 45°?
7. Round table Round table with diameter d = 105 cm is coated by square tablecloth with a side length 121 cm. About how many cm is higher center of tablecloth than its cornes?
8. Circle tangent It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p.
9. Square Rectangular square has side lengths 183 and 244 meters. How many meters will measure the path that leads straight diagonally from one corner to the other?
10. Annulus The radius of the larger circle is 8cm, the radius of smaller is 5cm. Calculate the contents of the annulus.
11. Angle in RT Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.
12. Percentage of waste In a square plate with side 75 cm we cut 4 same circles. Calculate the percentage of waste.
13. Meridian What is the distance (length) the Earth's meridian 23° when the radius of the Earth is 6370 km?
14. 6 regular polygon It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm2 (square centimeters) has a circle in which is inscribed the 6-gon.
15. Diagonal 20 Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
16. Rectangle vs square One side of the rectangle is 1 cm shorter than the side of the square, the second side is 3 cm longer than the side of the square. Square and rectangle have the same content. Calculate the length of the sides of a square and a rectangle.
17. Garage There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the garag
18. Vertices of RT Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
19. RT leg and perimeter Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.
20. 10 pieces How to divide the circle into 10 parts (geometrically)?

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