# 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.- 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. - 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. - Square and circles

Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles. - Ladder

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? - Trapezoid

Calculate area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm.. - N-gon angles

What is the sum of interior angles 8-gon? What is the internal angle of a regular convex 8-polygon? - Bicycle wheel

A bicycle wheel has a diameter of 60 cm. Approximately how many times does wheel rotate at 2.5 km long trip? - Triangle SSS

Calculate perimeter and area of a triangle ABC, if a=42, b=57 and c=42. - N-gon

How many diagonals has convex 11-gon? - Right triangle Alef

The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs. - 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. - 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. - Crossroads

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. - Quadrilateral prism

The surface of the regular quadrilateral prism is 8800 cm^{2}, the base edge is 20 cm long. Calculate the volume of the prism - 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. - 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 cm^{2}. What is the surface of the pyramid? - Height of pyramid

The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height? - Quadrilateral pyramid

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. - 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. - 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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See also more information on Wikipedia.