# 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. Triangle SAA The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
2. Triangles Equilateral triangle with side 40 cm has the same perimeter as an isosceles triangle with arm of 45 cm. Calculate the base x of an isosceles triangle.
3. Square and circles Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles. Ladder 8 m long is leaning against the wall. Its foot is 1 m away from the wall. In which height ladder touches the wall?
5. Trapezoid Calculate area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm..
6. N-gon angles What is the sum of interior angles 8-gon? What is the internal angle of a regular convex 8-polygon?
7. Bicycle wheel A bicycle wheel has a diameter of 60 cm. Approximately how many times does wheel rotate at 2.5 km long trip?
8. Triangle SSS Calculate perimeter and area of ​​a triangle ABC, if a=42, b=57 and c=42.
9. N-gon How many diagonals has convex 11-gon?
10. Right triangle Alef The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
11. Slope of track Calculate the average slope (in permille and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitrianske Pravno (354 m AMSL), if the track is 11 km long.
12. Right triangle Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm. Passenger car and an ambulance come to the rectangular crossroad, the ambulance left. Passenger car at speed 39 km/h and ambulance at 41 km/h. Calculate such a relative speed of the ambulance move to the car. The surface of the regular quadrilateral prism is 8800 cm2, the base edge is 20 cm long. Calculate the volume of the prism
15. Cutting cone A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.
16. Surface of pyramid In a regular quadrilateral pyramid, the height of the sidewall is equal to the length of the edge of the base. The content of the sidewall is 32 cm2. What is the surface of the pyramid?
17. Height of pyramid The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height? Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm.
19. Pentagonal prism The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
20. Triangular prism Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm.

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